How do you solve 5^(x+3)=6?

1 Answer
Nov 26, 2015

x = ln(6)/ln(5) - 3

Explanation:

We will use the property that
ln(a^x) = xln(a)


5^(x+3) = 6

=> ln(5^(x+3)) = ln(6)

=>(x+3)ln(5) = ln(6) " "(by the above property)

=> x + 3 = ln(6)/ln(5)

=> x = ln(6)/ln(5) - 3


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Note that we can easily check the answer by using the property ln(a)/ln(b) = log_b(a)

Then
5^(ln(6)/(ln(5))+3 - 3) = 5^(ln(6)/ln(5)) = 5^(log_5(6)) = 6