Question

100 Quick and EASY POINTS to make if you can help me!

Answer 1

Answer:

$x=125$

Step-by-step explanation:

We have the equation:

$\displaystyle \log_2{24}-\log_2{3}=\log_5x$

And we want to find the real value of x.

First, we can use the Quotient Property of Logarithms, which states:

$\displaystyle \log_ba-\log_bc=\log_b{\frac{a}{c}$

Therefore, we can rewrite our left-hand side as:

$\displaystyle \Rightarrow \log_2{\frac{24}{3}}=\log_5x$

Divide:

$\log_28=\log_5x$

Evaluate the left-hand side (2³=8).

$3=\log_5x$

By the definition of a logarithm, this means that:

$5^3=x$

Evaluate:

$x=125$

Our final answer is 125.

Answer 2

Answer:

x=125

Step-by-step explanation:

x>0, x=125

$log_{2} 8 = log_{5} x\\log_{2}2^{3} = log_{5} x\\3=log_{5} x\\log_{5} x=3\\x=5^{3} \\x=125$