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Question Number 151284 by mathdanisur last updated on 19/Aug/21

$$\mathrm{if}\frac{\mathrm{a}}{3^{\mathbf{x}-1}}=\frac{\mathrm{b}}{3^{\mathbf{y}+2}}=\frac{\mathrm{c}}{3^{\mathbf{z}-1}}=\frac{1}{5}$$$$\mathrm{find}\mathrm{abc}=?$$

Answered by Rasheed.Sindhi last updated on 19/Aug/21

$$\mathrm{a}=\frac{3^{\mathrm{x}-1}}{5},\mathrm{b}=\frac{3^{\mathrm{y}+2}}{5},\mathrm{c}=\frac{3^{\mathrm{z}-1}}{5}$$$$\mathrm{abc}=\left(\frac{3^{\mathrm{x}-1}}{5}\right)\left(\frac{3^{\mathrm{y}+2}}{5}\right)\left(\frac{3^{\mathrm{z}-1}}{5}\right)$$$$=\frac{3^{(\mathrm{x}-1)+(\mathrm{y}+2)+(\mathrm{z}-1)}}{125}=\frac{3^{\mathrm{x}+\mathrm{y}+\mathrm{z}}}{125}$$

Commented by mathdanisur last updated on 19/Aug/21

$$\mathrm{Thankyou}\mathrm{Ser}$$$$\mathrm{A}\mathrm{n}\mathrm{s}:\mathrm{a})1/125\mathrm{b})3/125\mathrm{c})27/125$$

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