Solve the following logarithmic equation.

Ask by Marshall Vaughn. in the United States

Jan 26,2025

Question

Solve the following logarithmic equation. $$ \begin{array}{l}\log _{10}(4 x)=2 \ x=15 \ x=30 \ x=20 \ x=25\end{array} $$

UpStudy AI · Accepted Answer

To solve the logarithmic equation:

$$
\log_{10}(4x) = 2
$$

**Step 1: Convert the logarithmic equation to its exponential form.**

Recall that $$\log_b(a) = c$$ is equivalent to $$b^c = a$$. Applying this to the given equation:

$$
10^2 = 4x
$$

**Step 2: Simplify the equation.**

$$
100 = 4x
$$

**Step 3: Solve for $$x$$.**

$$
x = \frac{100}{4} = 25
$$

**Conclusion:**

The correct value of $$x$$ that satisfies the equation $$\log_{10}(4x) = 2$$ is:

$$
\boxed{25}
$$
$$ x = 25 $$

Solve the following logarithmic equation.