Exponential and Logarithmic Equations

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

• add

• subtract

• multiply

• divide

When you have a log expression with a number in front of it, we really need to ___________ .

• make the number an exponent at the end of the log expression.

• multiply it with the log expression.

• add it to the log expression.

• subtract it from the log expression.

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

• add

• subtract

• multiply

• divide

Expand log_b(xy).

• log_bx+log_by

• log_bx-log_by

• log_bx*log_by

• log_bx/log_by

Expand log_b(x/y).

• log_bx-log_by

• log_bx+log_by

• log_bx*log_by

• log_bx/log_by

Rewrite log_b(xⁿ)

• nlog_bx

• (log_bx)ⁿ

• xⁿlog_bx

• log_b(xⁿ)

Write the expression as a single logarithm.   Then simplify if possible.
log₅3 + log₅6 + log₅9

• log₅69

• log₅56

• log₅162

• log₅98

Write the expression as a single logarithm.   Then simplify if possible.
log 6 - log 3 + 2 log 7

• log 98

• log 78

• log 56

• log 45

Use the properties of logarithms to rewrite as the sum of two logarithms:

 $\log55$  

• log 40 + log 15

• log 50 + log 5

• log 11 + log 5

Use the properties of logarithms to rewrite as the difference of two logs:

 $\log_545$  

•  $\log_590\ -\log_52$  

•  $\log_515-\log_53$  

•  $\frac{\log45}{\log\ 5}$  

•  $\log_550-\log_55$