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Answer :
To convert the logarithmic equation [tex]\(\log_b 69 = 3\)[/tex] to its exponential form, follow these steps:
1. Understand the logarithmic form:
[tex]\[
\log_b 69 = 3
\][/tex]
This equation means that the logarithm of 69 with base [tex]\(b\)[/tex] equals 3.
2. Recall the definition of logarithms:
The logarithmic equation [tex]\(\log_b a = c\)[/tex] is equivalent to the exponential equation [tex]\(b^c = a\)[/tex].
3. Identify the components:
[tex]\[
b \quad \text{is the base,}
\][/tex]
[tex]\[
69 \quad \text{is the result or the number we are taking the logarithm of,}
\][/tex]
[tex]\[
3 \quad \text{is the exponent.}
\][/tex]
4. Translate the logarithmic form to exponential form:
Using the definition, [tex]\(\log_b 69 = 3\)[/tex] can be rewritten as:
[tex]\[
b^3 = 69
\][/tex]
Therefore, the exponential form of [tex]\(\log_b 69 = 3\)[/tex] is:
[tex]\[
b^3 = 69
\][/tex]
1. Understand the logarithmic form:
[tex]\[
\log_b 69 = 3
\][/tex]
This equation means that the logarithm of 69 with base [tex]\(b\)[/tex] equals 3.
2. Recall the definition of logarithms:
The logarithmic equation [tex]\(\log_b a = c\)[/tex] is equivalent to the exponential equation [tex]\(b^c = a\)[/tex].
3. Identify the components:
[tex]\[
b \quad \text{is the base,}
\][/tex]
[tex]\[
69 \quad \text{is the result or the number we are taking the logarithm of,}
\][/tex]
[tex]\[
3 \quad \text{is the exponent.}
\][/tex]
4. Translate the logarithmic form to exponential form:
Using the definition, [tex]\(\log_b 69 = 3\)[/tex] can be rewritten as:
[tex]\[
b^3 = 69
\][/tex]
Therefore, the exponential form of [tex]\(\log_b 69 = 3\)[/tex] is:
[tex]\[
b^3 = 69
\][/tex]
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