Question
What is the exponential form of the equation log3(2x+5)=4?
Answers
GPT-4o mini
To convert the logarithmic equation \( \log_3(2x + 5) = 4 \) into its exponential form, we use the definition of logarithms, which states that if \( \log_b(a) = c \), then \( b^c = a \).
In this case:
- \( b = 3 \)
- \( c = 4 \)
- \( a = 2x + 5 \)
Applying the definition, we get:
\[
3^4 = 2x + 5
\]
Now, calculating \( 3^4 \):
\[
3^4 = 81
\]
Thus, the equation in exponential form is:
\[
81 = 2x + 5
\]
This is the exponential form of the original logarithmic equation.
In this case:
- \( b = 3 \)
- \( c = 4 \)
- \( a = 2x + 5 \)
Applying the definition, we get:
\[
3^4 = 2x + 5
\]
Now, calculating \( 3^4 \):
\[
3^4 = 81
\]
Thus, the equation in exponential form is:
\[
81 = 2x + 5
\]
This is the exponential form of the original logarithmic equation.