Answer:
[tex]x=125[/tex]
Step-by-step explanation:
We have the equation:
[tex]\displaystyle \log_2{24}-\log_2{3}=\log_5x[/tex]
And we want to find the real value of x.
First, we can use the Quotient Property of Logarithms, which states:
[tex]\displaystyle \log_ba-\log_bc=\log_b{\frac{a}{c}[/tex]
Therefore, we can rewrite our left-hand side as:
[tex]\displaystyle \Rightarrow \log_2{\frac{24}{3}}=\log_5x[/tex]
Divide:
[tex]\log_28=\log_5x[/tex]
Evaluate the left-hand side (2³=8).
[tex]3=\log_5x[/tex]
By the definition of a logarithm, this means that:
[tex]5^3=x[/tex]
Evaluate:
[tex]x=125[/tex]
Our final answer is 125.
