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

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

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

$$3^{x+2}=3^{x-1}\cdot 5^{x-1}$$$$3^{(x+2)-(x-1)}=5^{x-1}$$$$3^3\cdot 5=5^x$$$$\log \left(5^x\right)=\log (3^3\cdot 5)$$$$x\log 5=3\log 3+\log 5$$$$x=\frac{3\log 3+\log 5}{\log 5}$$

Commented by Mastermind last updated on 21/Jan/24

$$\mathrm{Thank}\mathrm{you}\mathrm{so}\mathrm{much},\mathrm{man}$$$$\mathrm{I}\mathrm{really}\mathrm{appreciate}$$

Answered by Skabetix last updated on 21/Jan/24

$$x={log}_5\left(135\right)$$

Commented by Mastermind last updated on 21/Jan/24

$$\mathrm{Thank}\mathrm{you}$$

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