solve the equation. 2 log₁₀(3x) = 4 x = ?

Explanation:

Step1: Isolate the logarithm

Divide both sides of the equation $2\log_{10}(3x)=4$ by 2. $\frac{2\log_{10}(3x)}{2}=\frac{4}{2}$ $\log_{10}(3x) = 2$

Step2: Convert to exponential form

By the definition of logarithms, if $\log_{a}b=c$, then $a^{c}=b$. Here $a = 10$, $c = 2$ and $b=3x$. $10^{2}=3x$ $100 = 3x$

Step3: Solve for x

Divide both sides of the equation $100 = 3x$ by 3. $x=\frac{100}{3}$

Answer:

$\frac{100}{3}$