Question

solve the equation. log 25 - log 4x = 1
x = (type an integer or a decimal.)

Explanation:

Step1: Apply log - subtraction rule

Using the rule $\log a-\log b = \log\frac{a}{b}$, the equation $\log 25-\log 4x = 1$ becomes $\log\frac{25}{4x}=1$.

Step2: Convert to exponential form

If $\log_{10}y = z$, then $y = 10^{z}$. So, $\frac{25}{4x}=10^{1}=10$.

Step3: Solve for x

Cross - multiply to get $25 = 10\times4x$. Then $25 = 40x$. Divide both sides by 40: $x=\frac{25}{40}=\frac{5}{8}=0.625$.

Answer:

$0.625$