Question

possible points: 42 b6
match each equation in logarithmic form to the equivalent equation in exponential form.
$log_{150} x = 5$
$log_{5} 150 = x$
$log_{x} 150 = 5$
$5^{x}=150$
$150^{5}=x$
$x^{5}=150$

Explanation:

Step1: Recall log-exponential rule

The logarithmic form $\log_b a = c$ converts to exponential form $b^c = a$.

Step2: Convert $\log_{150} x = 5$

Apply the rule: $b=150$, $c=5$, $a=x$
$150^5 = x$

Step3: Convert $\log_{5} 150 = x$

Apply the rule: $b=5$, $c=x$, $a=150$
$5^x = 150$

Step4: Convert $\log_{x} 150 = 5$

Apply the rule: $b=x$, $c=5$, $a=150$
$x^5 = 150$

Answer:

• $\boldsymbol{\log_{150} x = 5}$ matches $\boldsymbol{150^5 = x}$
• $\boldsymbol{\log_{5} 150 = x}$ matches $\boldsymbol{5^x = 150}$
• $\boldsymbol{\log_{x} 150 = 5}$ matches $\boldsymbol{x^5 = 150}$