How do you solve 5^(x+2)=4?

1 Answer
Jul 25, 2016

x = (2*(log 2 - log 5))/log 5

Explanation:

One of the logarithm rules one should keep in mind for this problem:

log a^b = b*loga

Apply logarithm on both sides

log(5^(x+2)) = log 4

=>(x+2)*log 5 = log 4

=>x+2 = log 4/log 5

Now it's just a matter of simplification:

=> x = log(2^2)/log 5 - 2

=>x = (2*log 2)/ log 5 - 2

=> x = (2*log 2 - 2 log 5)/log 5

or, x = (2*(log 2 - log 5))/log 5