How to use exponents instead of logs

Convert into same base

Step-by-step explanation:

Convert both sides into same bases and equate the powers to solve for the variable.

Example:

8^x = 32

You can either use logs to bring the power down or convert both sides into the same base

8 = 2³

8^x = (2³)^x = 2^(3x)

32 = 2⁵

2^(3x) = 2⁵

3x = 5

x = 5/3

x = 1⅔

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: