Find the exact value of the logarithmic expression without using a calculator.
A)3
C)7
D)21
E)None of these

Question

Find the exact value of the logarithmic expression without using a calculator. ​  ​
A)3 
C)7 
D)​21 
E)None of these

Quizplus · Accepted Answer

We can rewrite the given expression as:
$log_{8}(2^{19})$
Using the property of logarithms, we can bring the exponent outside:
$19log_{8}(2)$
Since $2^3=8$, we know that $log_{8}(2)=\frac{1}{3}$
Substituting this value, we get:
$19\cdot\frac{1}{3}=\frac{19}{3}$
Therefore, the exact value of the logarithmic expression is $\frac{19}{3}$ which can be represented as the given choice B in the hexadecimal format.

Find the Exact Value of the Logarithmic Expression Without Using