Checkpoint: Convert between Exponential and Logarithmic Equations Solutions

Convert the equation to its inverse (exponential to logarithmic or logarithmic to exponential).

Note

Problems A–B

Q: What is the base of the log in problem A? Problem B? 

A: The logarithmic base in problem A is 4. The logarithmic base in problem B is 64.

Q: If problem B were written in radical form, what would the index be? (Remember, the index is the number outside the radical that occurs when it is something other than a square root.)  

A: 6

$4^{3} = 64$

$\log_{4} 64 = 3$

$\log_{64} 32 = \frac{5}{6}$

$64^{\frac{5}{6}} = 32$