005 Sample Final A, Question 7

Question Solve the following equation,      $2\log _{5}(x)=3\log _{5}(4)$

Step 1
Use the rules of logarithms to move the 2 and the 3 to exponents. So $\log _{5}(x^{2})=\log _{5}(4^{3})$

Step 2
By the definition of logarithm, we find that $x^{2}=4^{3}$

Step 3
Taking the square root of both sides we get $x=8$

Final Answer
$x=8$