Question

solve the equation. log 25 - log 2x = 1
x = (type an integer or a decimal.)

Explanation:

Step1: Use log - rule

Apply the quotient - rule of logarithms $\log a-\log b=\log\frac{a}{b}$. So, $\log 25-\log 2x=\log\frac{25}{2x}$, and the equation becomes $\log\frac{25}{2x}=1$.

Step2: Convert to exponential form

If the base of the logarithm is 10 (common logarithm), and $\log_{10}y = a$ can be written as $y = 10^{a}$. Here, $\frac{25}{2x}=10^{1}=10$.

Step3: Solve for x

Cross - multiply to get $25 = 10\times(2x)$. Then $25=20x$. Divide both sides by 20: $x=\frac{25}{20}=\frac{5}{4}=1.25$.

Answer:

$1.25$