Question

I need help on how to answer this question

Answer 1

`2^(x+1)=9\implies \log(2^(x+1))=\log(9)\implies \log_(10)(2^(x+1))=\log_(10)(9) \\\\\\ \stackrel{ \textit{change of base rule} }{\cfrac{\log_2(2^(x+1))}{\log_2(10)}}=\log_(10)(9)\implies \cfrac{x+1}{\log_2(10)}=\log_(10)(9) \\\\\\ x+1=\log_(10)(9)\log_2(10)\implies x=\log_(10)(9)\log_2(10)-1\implies x\approx 2.170`

Answer 2

Answer: log (base 2)(9)=x+1

Explanation:

When you have logs like this you can do b^(logy/logb)=Y. This is the format that 2^(x+1)=9 is in. I hope this helps.