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Question Number 199486 by hardmath last updated on 04/Nov/23

$$\mathrm{Solve}:{100}^{\mathbf{x}}=200$$

Answered by cortano12 last updated on 04/Nov/23

$$\log {}_{10}\left({100}^{\mathrm{x}}\right)=\log {}_{10}\left(200\right)$$$$2\mathrm{x}=2+\log {}_{10}\left(2\right)$$$$\mathrm{x}=1+\log {}_{10}\left(\sqrt{2}\right)$$

Answered by Skabetix last updated on 04/Nov/23

$$xln\left(100\right)=ln\left(200\right)$$$$x=\frac{ln\left(200\right)}{ln\left(100\right)}=\frac{log\left(200\right)}{2}$$

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