Hi,

I know that this question can be solved by graphing the two sides (the answer is -1), but is there a way to do it without?

\(2\log\left(x+11\right)={\left(\frac{1}{2}\right)}^{x}\)

Thank you for your help!

Guest Jan 19, 2022

#1**0 **

We can say x+11=y and then write log(y)=(2^10)/(2^y). From this we can observe that lince log is log_10, that if y is 10, then both sides have a value of 1. Since x+11=y, x=y-11, and x=-1. This is the way I would've done it without graphing but I am sure there might be an easier version to understand for solving this.

ImDecentAtMath Jan 19, 2022