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Question Number 146532 by mathdanisur last updated on 13/Jul/21

$$2^{\mathit{x}}=5,3^{\mathit{y}}=9and{25}^{\mathit{z}}=8$$$$find(x\cdot y\cdot z)=?$$

Answered by puissant last updated on 13/Jul/21

$${\mathrm{e}}^{\mathrm{xln}2}=5\Rightarrow \mathrm{x}=\frac{\ln 5}{\ln 2}$$$${\mathrm{e}}^{\mathrm{yln}3}=9\Rightarrow \mathrm{y}=\frac{2\ln 3}{\ln 3}=2$$$${\mathrm{e}}^{\mathrm{zln}25}=8\Rightarrow \mathrm{z}=\frac{3\ln 2}{2\ln 5}$$$$(\mathrm{x}\cdot \mathrm{y}\cdot \mathrm{z})=\frac{\ln 5}{\ln 2}\times \frac{3\ln 2}{2\ln 5}\times 2=3..$$

Commented by mathdanisur last updated on 13/Jul/21

$$coolthanksSer$$

Answered by Rasheed.Sindhi last updated on 14/Jul/21

$$2^{\mathit{x}}=5,3^{\mathit{y}}=9and{25}^{\mathit{z}}=8$$$$\underset{-}{x\cdot y\cdot z=?}$$$${25}^{\mathit{z}}=8\Rightarrow 5^{2z}=8\Rightarrow {\left(2^x\right)}^{2z}=2^3$$$$\Rightarrow 2xz=3\Rightarrow xz=\frac{3}{2}....\left(i\right)$$$$3^y=9\Rightarrow 3^y=3^2\Rightarrow y=2.............\left(ii\right)$$$$\left(i\right)\times \left(ii\right):xyz=\left(\frac{3}{2}\right)\left(2\right)=3$$

Commented by mathdanisur last updated on 14/Jul/21

$$thanksSercool$$

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