How do you solve 7.74^(x + 3) = 10.2?

1 Answer
Nov 22, 2015

I found: x-1.8651

Explanation:

You can first take the natural log of both sides:

ln(7.74)^(x+3)=ln(10.2)

Then you can use the property of logs that tells us that:

logx^b=blogx

and write:

(x+3)ln(7.74)=ln(10.2)
rearrange:

x+3=(ln(10.2))/ln(7.74)
x=(ln(10.2))/ln(7.74)-3
x=1.1348-3=-1.8651