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Question Number 159345 by akolade last updated on 15/Nov/21

Answered by Ar Brandon last updated on 15/Nov/21

$$5^{\frac{\mathrm{y}}{2}+3}=125\left(5^{\frac{\mathrm{y}}{2}}\right)=125{\left(5^{\mathrm{y}}\right)}^{\frac{1}{2}}$$$$=125{\left(36\right)}^{\frac{1}{2}}=125\times 6=750$$

Commented by akolade last updated on 15/Nov/21

$$\mathrm{cool}\mathrm{sir}$$

Answered by yeti123 last updated on 16/Nov/21

$$5^y=36$$$$y={\log }_{5}36$$$$$$$$x=5^{\frac{y}{2}+3}$$$${\log }_{5}x={\log }_5\left(5^{\frac{y}{2}+3}\right)$$$$=(\frac{y}{2}+3){\log }_{5}5$$$$=\frac{y}{2}+3$$$$=\frac{1}{2}{\log }_{5}36+3$$$$={\log }_5{36}^{1/2}+{\log }_5{5}^3$$$$={\log }_{5}6+{\log }_{5}125$$$$={\log }_5\left(6\times 125\right)$$$$x=6\times 125$$$$=750$$

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