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Question Number 215089 by golsendro last updated on 28/Dec/24

$$\log {}_2\mathrm{x}+\log {}_3(\mathrm{x}+1)=5$$$$\mathrm{x}=?$$

Answered by efronzo1 last updated on 28/Dec/24

$$\log {}_3(\mathrm{x}+1)-2=3-\log {}_2\mathrm{x}$$$$\log {}_3\left(\frac{\mathrm{x}+1}{9}\right)=\log {}_2\left(\frac{8}{\mathrm{x}}\right)$$$$\log {}_3\left(1\right)=\log {}_2\left(1\right)=0$$$$\frac{\mathrm{x}+1}{9}=1\mathrm{and}\frac{8}{\mathrm{x}}=1$$$$\mathrm{x}=8$$

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