Question

Help pleaseeee :,) 100 points

Answer 1

Answer: J) 125

Explanation:

Answer 2

Answer:

x = 125

Step-by-step explanation:

Given equation:

$\log_224-\log_23=\log_5x$

$\textsf{Apply the Quotient log law}: \quad \log_ax - \log_ay=\log_a\frac{x}{y}$

$\implies \log_2\left(\dfrac{24}{3}\right)=\log_5x$

$\implies \log_28=\log_5x$

Rewrite 8 as 2³:

$\implies \log_2(2^3)=\log_5x$

$\textsf{Apply the Power log law}: \quad \log_ax^n=n\log_ax$

$\implies 3\log_22=\log_5x$

$\textsf{Apply log law}: \quad \log_aa=1$

$\implies 3(1)=\log_5x$

$\implies \log_5x=3$

$\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b$

$\implies 5^3=x$

$\implies x=125$