How do you solve 5^ { x + 2} = 5^ { 9} ?

1 Answer
May 6, 2017

x= 7

Explanation:

When the base number on the LEFT-hand side equals to the base number on the RIGHT-hand side, we can simply equate their exponents/power.

http://www.softschools.com/math/topics/exponents/http://www.softschools.com/math/topics/exponents/

5^(x+2) = 5^9

By equating the exponents on the LHS and RHS, we get:

x+2 = 9
color(red)(x= 7)

Double checking the solution,

5^(7+2) = 5^9
5^9 = 5^9 Hurray!

Alternatively , we can use the logarithm to solve.
By adding log_5 to both sides, we get:

log_5 5^(x+2) = log_5 5^9

The special properties of logarithmic functions allow us to "bring" down the exponent as such:

(x+2) log_5 5 = 9log_5 5

When the base b, of the logarithmic functions is the same as the number, log_b b = 1.

Therefore, (x+2) x 1 = 9 x 1

x+2 = 9
color(red)(x=7)

Same as the previous answer!