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Question Number 158884 by akolade last updated on 10/Nov/21

Answered by ghimisi last updated on 10/Nov/21

$${log}_3(a+1)={log}_4(a+8)=t\Rightarrow$$$$a+1=3^t$$$$a+8=4^t\Rightarrow 4^t-3^t=7\Rightarrow {\left(\frac{4}{3}\right)}^t=1+7\cdot {\left(\frac{1}{3}\right)}^t$$$$f\left(t\right)={\left(\frac{4}{3}\right)}^t\nearrow ;g\left(t\right)=1+7\cdot {\left(\frac{1}{3}\right)}^t\searrow$$$$\Rightarrow t=2\Rightarrow a=8$$

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