Question(a) Rewrite as a logarithmic equation. $5^{-2}=\frac{1}{25}$ (b) Rewrite as an exponential equation. $\log _{2} 16=4$

Studdy Solution

STEP 1

1. We are given an exponential equation and need to convert it to a logarithmic form.
2. We are given a logarithmic equation and need to convert it to an exponential form.
3. Understanding the relationship between logarithms and exponents is key.

STEP 2

1. Convert the exponential equation $5^{-2}=\frac{1}{25}$ to a logarithmic equation.
2. Convert the logarithmic equation $\log _{2} 16=4$ to an exponential equation.

STEP 3

Recall the definition of a logarithm: If $a^b = c$ , then $\log_a c = b$ .
Apply this definition to the given exponential equation $5^{-2}=\frac{1}{25}$ .
The base $a$ is 5, the exponent $b$ is $-2$ , and the result $c$ is $\frac{1}{25}$ .
Thus, the logarithmic form is:
$\log_5 \left(\frac{1}{25}\right) = -2$

STEP 4

Recall the definition of an exponential equation: If $\log_a c = b$ , then $a^b = c$ .
Apply this definition to the given logarithmic equation $\log _{2} 16=4$ .
The base $a$ is 2, the logarithm result $b$ is 4, and the number $c$ is 16.
Thus, the exponential form is:
$2^4 = 16$

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