# Use the One-to-One Property to solve the equation for .

**MATH**

** Use the properties of logarithms to expand the expression as a sum,…**

Expand by using subtraction, Given, Then, expanding and bringing down the exponent where necessary,

**MATH**

** Use the properties of logarithms to expand the expression…**

Expand using subtraction because the terms inside the log are being divided. Given, Then, Therefore, after bring down the…

**MATH**

** Use the properties of logarithms to expand the expression as…**

Expand using subtraction because the terms are being divided in the ln. Given, Then, after expanded and bringing down the exponents where necesarry

**MATH**

** Use the properties of logarithms to expand the expression as a…**

Since all of the terms are multiplied together, one can expand by adding them together. Given, Then,

**MATH**

** Use the properties of logarithms to expand the expression as a sum,…**

Since all of the terms are multiplied, one can just expand by adding them all. Given, Then, Separate all of the terms and bring the exponents down in front where necessary….

**MATH**

** Use the properties of logarithms to expand the expression as a sum, difference,…**

Since all of the terms are being multiplied inside the ln, that means to expand them, one must rewrite them as added. Therefore, Given Then,

**MATH**

** Use the properties of logarithms to expand the expression as a sum,…**

Rewrite as Bring down the exponent,

**MATH**

** Use the properties of logarithms to expand the expression as a sum,…**

Bring down the exponent, Therefore,

**MATH**

** Use the properties of logarithms to expand the expression as a sum,…**

Expand using subtraction, Bring down the exponent,

**MATH**

** Use the properties of logarithms to expand the expression as a sum,…**

Expand using subtraction,

**MATH**

** Use the properties of logarithms to expand the expression as a sum,…**

Expand by using subtraction,

**MATH**

** Use the properties of logarithms to expand the expression as a sum,…**

Bring down the exponent, Done. You cannot expand this log any further.

**MATH**

** Use the properties of logarithms to expand the expression as a sum,…**

Expand using addition,

**MATH**

** Use the properties of logarithms to expand the expression as a sum, difference, and…**

Expand using addition,

**MATH**

** Find the exact value of logarithmic expression without using a…**

Given, Condense, Set equal to x

**MATH**

** Find the exact value of logarithmic expression without using a…**

Given, Condense Set equal to x

**MATH**

** Find the exact value of logarithmic expression without using a…**

Bring down the exponents, Remember that Therefore, Simplify,

**MATH**

** Find the exact value of logarithmic expression without using a…**

Bring down the exponents, Remember that Therefore, Simplify,

**MATH**

** Find the exact value of logarithmic expression without using a…**

Rewrite, Bring down the exponent, Remember that Simplify,

**MATH**

** Find the exact value of logarithmic expression without using a calculator….**

Rewrite Bring down the exponent Remember that Simplify,

**MATH**

** Find the exact value of logarithmic expression without using a calculator. (If…**

Bring down the exponent Remember than simplify,

**MATH**

** Find the exact value of logarithmic expression without using a calculator. (If…**

Bring down the exponent Remember that Simplify,

**MATH**

** Find the exact value of logarithmic expression without using a calculator. (If…**

The value of log_3(-27) is not defined,because the domain of a logarithmic function does not include negative values.

**MATH**

** Find the exact value of logarithmic expression without using a calculator. (If…**

The value of is not defined,because the domain of a logarithmic function does not include negative values.

**MATH**

** Find the exact value of logarithmic expression without using a calculator….**

**MATH**

** Find the exact value of logarithmic expression without using a calculator….**

**MATH**

** Find the exact value of logarithmic expression without using a…**

log_6(6^(1/3))=(1/3)log_6(6) =0.333

**MATH**

** Find the exact value of logarithmic expression without using a…**

**MATH**

** Find the exact value of logarithmic expression without using a calculator….**

Rewrite log5 1/125 : This gives: , bring down the power , rewrite 125 in term of power of 5 , again…

**MATH**

** Find the exact value of logarithmic expression without using a calculator. (If…**

Set Rewrite,

**MATH**

** Use the properties of logarithms to rewrite and simplify the logarithmic…**

When you divide inside the ln, you subtract when you expand Bring down the exponent and remember than

**MATH**

** Use the properties of logarithms to rewrite and simplify the logarithmic expression.**

Expand using addition bring down the exponent Remember that

**MATH**

** Use the properties of logarithms to rewrite and simplify the logarithmic…**

**MATH**

** Use the properties of logarithms to rewrite and simplify the logarithmic…**

**MATH**

** Use the properties of logarithms to rewrite and simplify the logarithmic…**

**MATH**

** Use the properties of logarithms to rewrite and simplify the logarithmic…**

You need to use a change of base formula to solve this. Use since both and and powers of ) This simplifies down to,

**MATH**

** Evaluate the logarithm using the change-of-base formula. Round your result…**

…

**MATH**

** Evaluate the logarithm using the change-of-base formula. Round your result to…**

=-1.048

**MATH**

** Evaluate the logarithm using the change-of-base formula. Round your result…**

**MATH**

** Evaluate the logarithm using the change-of-base formula. Round your result to…**

log_3(7) = (log_(10)(7))/(log_(10)(3)) = (0.8451)/(0.4771) =1.771

**MATH**

** Rewrite the logarithm as a ratio of (a) common logarithms and (b) natural…**

(a) Common logarithms (b) natural logarithms …

**MATH**

** Rewrite the logarithm as a ratio of (a) common logarithms and (b) natural…**

(a) Common logarithms (b) natural logarithms …

**MATH**

** Rewrite the logarithm as a ratio of (a) common logarithms and (b) natural…**

Answer updated

**MATH**

** Rewrite the logarithm as a ratio of (a) common logarithms and (b) natural…**

Common logarithmslog 5 16 = (log 10 16) / (log 10 5) Natural Logarithmslog 5 16 = (ln 16) / (ln 5)

**MATH**

** Use the One-to-One Property to solve the equation for .**

Since there are ln’s on both side, they cancel and set the two parts equal to each other. Solve for x Factor and

**MATH**

** Use the One-to-One Property to solve the equation for .**

Since there are ln’s on both sides, set the terms equal to each other. Solve for x Factor and

**MATH**

** Use the One-to-One Property to solve the equation for .**

Since there are ln’s on both sides, set the terms equal to each other. Solve for x

**MATH**

** Use the One-to-One Property to solve the equation for .**

Since there are ln’s on both sides, set the terms equal to each other. Solve for x

**MATH**

** Evaluate at the indicated value of without using a…**

Plug in the value of x in Bring down the exponent Remember that Simplify,

**MATH**

** Evaluate at the indicated value of without using a…**

Plug in the value for x in Bring down the exponent Remember that Simplify,