Question

log₂4x - log₂3 = 1

Explanation:

Step1: Apply log subtraction rule

Using the logarithmic property $\log_a M - \log_a N=\log_a \frac{M}{N}$, we rewrite the left - hand side of the equation $\log_2 4x-\log_2 3 = 1$ as $\log_2\frac{4x}{3}=1$.

Step2: Convert logarithmic to exponential form

Recall that if $\log_a b = c$, then $b=a^c$. For the equation $\log_2\frac{4x}{3}=1$, we have $\frac{4x}{3}=2^1$.

Step3: Solve for x

Simplify the right - hand side: $2^1 = 2$. So the equation becomes $\frac{4x}{3}=2$. Multiply both sides by 3: $4x=2\times3 = 6$. Then divide both sides by 4: $x=\frac{6}{4}=\frac{3}{2}$.

Answer:

$x = \frac{3}{2}$