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Question Number 210607 by peter frank last updated on 13/Aug/24

Answered by A5T last updated on 14/Aug/24

$$75\left(5^{3{log}_{2}x}\right)=75{\left(2^{{log}_{2}5}\right)}^{{log}_{2}x\times 3}=75{\left(2^{{log}_{2}x}\right)}^{3{log}_{2}5}$$$$=75{\left(x\right)}^{3{log}_{2}5}=4x$$$$\Rightarrow x^{{log}_2\left(\frac{125}{2}\right)}=\frac{4}{75}\Rightarrow x={\left(\frac{4}{75}\right)}^{\frac{1}{{log}_2\left(125\right)-1}}\approx 0.6118$$

Commented by peter frank last updated on 14/Aug/24

Commented by peter frank last updated on 14/Aug/24

$$\mathrm{where}\mathrm{did}\mathrm{that}2\mathrm{come}\mathrm{from}?$$

Commented by A5T last updated on 14/Aug/24

$$b=a^{{log}_{a}b}\Rightarrow 5=2^{{log}_{2}5}$$

Answered by Spillover last updated on 14/Aug/24

Answered by Spillover last updated on 14/Aug/24

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