Answer: [tex]\bold{x=\dfrac{1-log_5(8)}{2}}[/tex]
Step-by-step explanation:
[tex]4^2\cdot 5^{2x}=10\\\\\\\text{divide both sides by }4^2=16:\\5^{2x}=\dfrac{10}{16}\\\\\\\text{reduce the fraction:}\\5^{2x}=\dfrac{5}{8}\\\\\\\text{apply }log_5\text{ to both sides:}\\ log_5(5)^{2x}=log_5\bigg(\dfrac{5}{8}\bigg)\\\\\\\text{cancel out }log_5(5):\\2x=log_5\bigg(\dfrac{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)[/tex]
[tex]\text{Divide 2 from both sides to solve for x:}\\\\x=\dfrac{1-log_5(8)}{2}[/tex]
