Question Number 165136 by saboorhalimi last updated on 26/Jan/22
Answered by MJS_new last updated on 26/Jan/22
$$\mathrm{obviously}\:{a}=\mathrm{8} \\ $$$$\mathrm{log}_{\mathrm{3}} \:\mathrm{9}\:=\mathrm{log}_{\mathrm{4}} \:\mathrm{16}\:=\mathrm{2} \\ $$
Commented by saboorhalimi last updated on 26/Jan/22
$${Solution}? \\ $$
Commented by MJS_new last updated on 26/Jan/22
$$\mathrm{no}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{method}\:\mathrm{exists} \\ $$
Answered by mahdipoor last updated on 26/Jan/22
$$\Rightarrow\mathrm{4}^{{t}} −\mathrm{3}^{{t}} ={a}+\mathrm{8}−\left({a}+\mathrm{1}\right)=\mathrm{7} \\ $$$$\Rightarrow{t}=\mathrm{2}\: \\ $$$$\mathrm{4}^{{t}} =\mathrm{16}={a}+\mathrm{8}\Rightarrow{a}=\mathrm{8} \\ $$
Answered by kapoorshah last updated on 26/Jan/22
$$\mathrm{log}\:_{\mathrm{3}} \:\mathrm{4}\:=\:\mathrm{log}\:_{\left({a}\:+\:\mathrm{1}\right)\:\:\:\:} \left({a}\:+\:\mathrm{8}\right) \\ $$$${a}\:+\:\mathrm{1}\:=\:\mathrm{3}^{\mathrm{2}} \\ $$$${a}\:+\:\mathrm{8}\:=\:\mathrm{4}^{\mathrm{2}} \\ $$$${a}\:=\:\mathrm{8} \\ $$$$ \\ $$
Commented by saboorhalimi last updated on 26/Jan/22
$${how}\:{could}\:{you}\:{change}\:{it}\:{into}\:{this} \\ $$$${form} \\ $$