Asked by Nieajua Gonzalez on May 21, 2024
Verified
Evaluate the logarithm. log51125\log _ { 5 } \frac { 1 } { 125 }log51251
A) 3\sqrt { 3 }3
B) -3
C) 0
D) 13\frac { 1 } { 3 }31
E) log51125\log _ { 5 } \frac { 1 } { 125 }log51251 is undefined.
Fraction
A numerical quantity that is not whole, representing a part of a whole.
Logarithm
A logarithm is the power to which a number, called the base, must be raised to produce a given number.
- Inspect fundamental and widespread logarithms, incorporating the utilization of principles of logarithms.
Verified Answer
NV
Nguyen Viet Thien (K14 HCM)May 21, 2024
Final Answer :
B
Explanation :
Remember that $\log_{5} \left(\frac{1}{125}\right) = x$ can be rewritten as $5^{x} = \frac{1}{125}$. We know that $125$ can be written as $5^{3}$, so we have $5^{x} = \frac{1}{5^{3}} = 5^{-3}$. Thus, $x = -3$. Therefore, the answer is $\boxed{\textbf{(B)}\ -3}$.
Learning Objectives
- Inspect fundamental and widespread logarithms, incorporating the utilization of principles of logarithms.