Write the equation in its equivalent logarithmic form.
-$$5 - 2 = \frac { 1 } { 25 }$$
A) $\log _ { 5 } \frac { 1 } { 25 } = - 2$
B) $\log _ { 1 / 5 } 5 = - 2$
C) $\log _ { - 2 } \frac { 1 } { 25 } = 5$
D) $\log _ { 5 } - 2 = \frac { 1 } { 25 }$

Question

Quizplus · Accepted Answer

The equation can be simplified to:

$$3 = \frac{1}{25}$$

Taking the logarithm base 5 of both sides, we get:

$$\log_{5}3 = \log_{5}\frac{1}{25}$$

Using the property of logarithms that states log(a/b) = log(a) - log(b), we can simplify the right-hand side:

$$\log_{5}3 = \log_{5}1 - \log_{5}25$$
$$\log_{5}3 = 0 - 2$$

Therefore, the equivalent logarithmic form of the equation is:

$$\log _ { 5 } \frac{1}{25} = -2$$

Write the Equation in Its Equivalent Logarithmic Form 5−2=1255 - 2 = \frac { 1 } { 25 }5−2=251​

Write the Equation in Its Equivalent Logarithmic Form $5 - 2 = \frac { 1 } { 25 }$