The given expression is
[tex]2\log _75+\log _7x=\log _7100[/tex]First, we have to use the power property of logarithms, which states
[tex]a\log x=\log x^a[/tex]So, we have
[tex]\log _75^2+\log _7x=\log _7100[/tex]Now, we use the product property of logarithm, which states
[tex]\log a+\log b=\log a\cdot b[/tex]Then, we have
[tex]\log _75^2\cdot x=\log _7100[/tex]We can eliminate logarithms
[tex]5^2\cdot x=100[/tex]Now, we solve for x
[tex]\begin{gathered} 25x=100 \\ x=\frac{100}{25}=4 \end{gathered}[/tex]