Power Property of Logarithms Problems

Write the approximate value that solves the exponential equation, rounded to the third decimal place (for example, 1.234).

 $1.5^x=9$  

(a)  

Answer explanation

 $\log\left(1.5^x\right)=\log\left(9\right)$  , so  $x=\frac{\log9}{\log1.5}\approx5.4190...$  

Write the approximate value that solves the exponential equation, rounded to the thousandths place (for example, 1.234).

 $3^x=7.9$  

(a)  

Answer explanation

 $\log\left(3^x\right)=\log\left(7.9\right)$  , so  $x=\frac{\log\left(7.9\right)}{\log\left(3\right)}\approx1.8813...$  

Write the approximate value that solves the logarithmic equation, rounded to the third decimal place (for example, 1.234).

 $y=\log_{3.7}\left(9\right)$  

(a)  

Answer explanation

 $3.7^y=9$  , and if you apply the common log to both sides,  $\log\left(3.7^y\right)=\log\left(9\right)$  .  Then  $y=\frac{\log\left(9\right)}{\log\left(3.7\right)}\approx1.6794...$  

Write the approximate value that solves the logarithmic equation, rounded to the third decimal place (for example, 1.234).

 $y=\log_2\left(10\right)$  

(a)  

Answer explanation

 $2^y=10$  , and if you apply the common log to both sides,  $\log\left(2^y\right)=\log\left(10\right)=1$  .  Then  $y=\frac{1}{\log\left(2\right)}\approx3.32192...$  

Write the approximate value that solves the exponential equation, rounded to the third decimal place (for example, 1.234).

 $5^x=12$  

(a)  

Answer explanation

 $\log\left(5^x\right)=\log\left(12\right)$  , so  $x=\frac{\log\left(12\right)}{\log\left(5\right)}\approx1.5439...$  

Write the EXACT value that solves the logarithmic equation 

 $y=2\cdot\log_3\left(9\right)$  

(a)  

Answer explanation

If we apply the power rule of logs,  $y=\log_3\left(9^2\right)$ .  So   $y=\log_381$  written as an exponential is   $3^y=81$  , and  $y=4.$