Question

State true or false:

${\log }_a{x}^n=n{\log }_{a}x$

• A. True
• B. False

Answer 1

The correct option is A True

Step 1:

Let $m={\log }_{a}x$

Step 2: Write in exponent form

$x=a^m$

Step 3: Raise both sides to the power of $n$

$x^n=(a^m{)}^n$

Step 4: Convert back to a logarithmic equation

${\log }_a{x}^n=mn$

Step 5: Substitute for $m={\log }_{a}x$

${\log }_a{x}^n=n{\log }_{a}x$