How do you solve #5^ { - 3x - 3} = 625#?

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Answer 1 · 2017-06-06T00:57:14

#x = -7/3#

First, take the #log_5# of both sides.

#5^(-3x-3) = 625#

#5^(-3x-3) = 5^4#

#log_5(5^(-3x-3)) = log_5(5^4)#

The logarithm and the base cancel out:

#color(red)cancel(log_5)(color(red)(cancel5)^(-3x-3)) =color(red)cancel(log_5)(color(red)(cancel5)^4) #

#-3x-3 = 4#

Now, use normal algebra to solve for #x#:

#-3x = 7#

#x = -7/3#

Final Answer