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Question Number 193363 by MATHEMATICSAM last updated on 11/Jun/23

$$y=4\times {10}^{2x}$$$$\mathrm{Express}x\mathrm{in}\mathrm{terms}\mathrm{of}y,\mathrm{giving}\mathrm{an}\mathrm{exact}$$$$\mathrm{simplified}\mathrm{answer}\mathrm{in}\mathrm{terms}\mathrm{of}\log \mathrm{base}10.$$

Answered by aba last updated on 11/Jun/23

$$\mathrm{y}=4\times {10}^{2\mathrm{x}}\Rightarrow {10}^{2\mathrm{x}}=\frac{\mathrm{y}}{4}\Rightarrow \mathrm{x}=\frac{1}{2}{\log }_{10}\left(\frac{\mathrm{y}}{4}\right)$$

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