Question

Solve this, thanks!

`{4}^(2) ( {5}^(2x) ) = 10`
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Answer 1

Answer:
`\bold{x=(1-log_5(8))/(2)}`

Explanation:

`4^2\cdot 5^(2x)=10\\\\\\\text{divide both sides by }4^2=16:\\5^(2x)=(10)/(16)\\\\\\\text{reduce the fraction:}\\5^(2x)=(5)/(8)\\\\\\\text{apply }log_5\text{ to both sides:}\\ log_5(5)^(2x)=log_5\bigg((5)/(8)\bigg)\\\\\\\text{cancel out }log_5(5):\\2x=log_5\bigg((5)/(8)\bigg)\\\\\\\text{Apply the division rule for logs:}\\2x=log_5(5)-log_5(8)\\\\\\\text{Simplify }log_5(5)=1:\\2x=1-log_5(8)`

`\text{Divide 2 from both sides to solve for x:}\\\\x=(1-log_5(8))/(2)`