Question

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Answer 1

`\large\boxed{x\approx0.52}`

Explanation:

`2^(5x)=6\Rightarrow\log_22^(5x)=\log_26\qquad\text{use}\ \log_ab^n=n\log_ab\\\\5x\log_22=\log_26\qquad\text{use}\ \log_aa=1\\\\5x=\log_26\qquad\text{divide both sides by 5}\\\\x=(\log_26)/(5)\\\\\log_26\approx2.585\\\\x\approx(2.585)/(5)\to\boxed{x\approx0.52}`