Question
which equation is equivalent to 2^3x =10
log 2 = 3x
log 3x =2
log2 3x =10
log2 10=3x
log 2 = 3x
log 3x =2
log2 3x =10
log2 10=3x
Answers
Answered by
GPT-4o mini
To solve the equation \(2^{3x} = 10\), we can take the logarithm of both sides. Using the change of base property of logarithms, we can express the equation in logarithmic form.
Let's rewrite the equation step-by-step:
1. Start with \(2^{3x} = 10\).
2. Taking logarithm base 2 of both sides:
\[
\log_2(2^{3x}) = \log_2(10)
\]
3. By the power rule of logarithms, we have:
\[
3x = \log_2(10)
\]
From this, we find that the equivalent equation is:
\[
\log_2(10) = 3x
\]
Thus, among the given options, the correct answer is:
\[
\log_2(10) = 3x
\]
Let's rewrite the equation step-by-step:
1. Start with \(2^{3x} = 10\).
2. Taking logarithm base 2 of both sides:
\[
\log_2(2^{3x}) = \log_2(10)
\]
3. By the power rule of logarithms, we have:
\[
3x = \log_2(10)
\]
From this, we find that the equivalent equation is:
\[
\log_2(10) = 3x
\]
Thus, among the given options, the correct answer is:
\[
\log_2(10) = 3x
\]