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

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Answer 1 · 2016-07-25T15:11:46

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

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:

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

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

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

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

How do you solve 5^(x+2)=45^(x+2)=4?