The state that a and a with the same base undo each other. Let's use this to solve the equation.
log5(x)=2 5LHS=5RHS 5log5(x)=52 5log5(m)=m
Here we can use the same method.
log4(x)=-1 4LHS=4RHS 4log4(x)=4-1 4log4(m)=m x=4-1
Here we first need to isolate the logarithm on the left-hand side.
5log2(x)+80=100 5log2(x)=20 log2(x)=4 2LHS=2RHS 2log2(x)=24 2log2(m)=m
Just like in the previous exercise we first need to isolate the logarithm before we can undo it using the inverse properties of logarithms.
2log7(2x)=1 log7(2x)=2 7LHS=7RHS 7log7(2x)=72 7log7(m)=m