Solve-for-x-3-x-2-15-x-1-

Question Number 203533 by Mastermind last updated on 21/Jan/24

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:: \\ $$$$\mathrm{3}^{\mathrm{x}+\mathrm{2}} =\mathrm{15}^{\mathrm{x}−\mathrm{1}} \\ $$

Answered by Rasheed.Sindhi last updated on 21/Jan/24

3^(x+2) =3^(x−1) ∙5^(x−1) 3^((x+2)−(x−1)) =5^(x−1) 3^3 ∙5=5^x log(5^x )=log(3^3 ∙5) xlog5=3log3+log5 x=((3log3+log5)/(log5 ))

$$\mathrm{3}^{{x}+\mathrm{2}} =\mathrm{3}^{{x}−\mathrm{1}} \centerdot\mathrm{5}^{{x}−\mathrm{1}} \\ $$$$\mathrm{3}^{\left({x}+\mathrm{2}\right)−\left({x}−\mathrm{1}\right)} =\mathrm{5}^{{x}−\mathrm{1}} \\ $$$$\mathrm{3}^{\mathrm{3}} \centerdot\mathrm{5}=\mathrm{5}^{{x}} \\ $$$$\mathrm{log}\left(\mathrm{5}^{{x}} \right)=\mathrm{log}\left(\mathrm{3}^{\mathrm{3}} \centerdot\mathrm{5}\right) \\ $$$${x}\mathrm{log5}=\mathrm{3log3}+\mathrm{log5} \\ $$$${x}=\frac{\mathrm{3log3}+\mathrm{log5}}{\mathrm{log5}\:}\:\:\: \\ $$

Commented by Mastermind last updated on 21/Jan/24