Question

Solve for yLog 5 + log y = log 40

Answer 1

ANSWER

y = 8

EXPLANATION

To solve this equation, first, we have to apply the product property of logarithms,

$\log(ab)=\log a+\log b$

In this equation we have the right side of the property written above, so applying this rule we have,

$\begin{gathered} \log5+\log y=\log40 \\ \\ \log(5y)=\log40 \end{gathered}$

If two logarithms have the same base and are equal, then their arguments are equal,

$5y=40$

Finally, divide both sides by 5,

$\begin{gathered} \frac{5y}{5}=\frac{40}{5} \\ \\ y=8 \end{gathered}$

Hence, the solution is y = 8.