Please help asap! These two have been a struggle for me...

Answer:
A
C
Step-by-step explanation:
recall the following rule:
[tex]n^x=y\\log_ny=x[/tex]
to solve the first one we have
[tex]40(10^x)=15\\10^x=\frac{15}{40}\\x=log(\frac{15}{40})[/tex]
This is equal to
[tex]\frac{log\frac{15}{40}}{log10}[/tex] or A
same deal for the second one
[tex]10^x=\frac{25}{50}\\x=log{\frac{25}{50}=\frac{log(\frac{25}{50})}{log10}[/tex] or C