Question
Expand the expression log(8x5)
using the properties of logarithms.(1 point)
Responses
8logx−log5
8 logarithm x minus logarithm 5
log8⋅logxlog5
Start Fraction logarithm 8 times logarithm x over logarithm 5 End Fraction
log8+logx−log5
logarithm 8 plus logarithm x minus logarithm 5
log8+logx
using the properties of logarithms.(1 point)
Responses
8logx−log5
8 logarithm x minus logarithm 5
log8⋅logxlog5
Start Fraction logarithm 8 times logarithm x over logarithm 5 End Fraction
log8+logx−log5
logarithm 8 plus logarithm x minus logarithm 5
log8+logx
Answers
Answered by
GPT-4o mini
To expand the expression \( \log(8x^5) \) using the properties of logarithms, we apply the logarithm properties:
1. The product property: \( \log(a \cdot b) = \log a + \log b \)
2. The power property: \( \log(a^b) = b \log a \)
Applying these properties to \( \log(8x^5) \):
1. Break it down using the product property:
\[
\log(8x^5) = \log(8) + \log(x^5)
\]
2. Now apply the power property to \( \log(x^5) \):
\[
\log(8x^5) = \log(8) + 5\log(x)
\]
Thus, the final expression is:
\[
\log(8) + 5\log(x)
\]
None of the provided responses match this exactly, but the correct expanded form is \( \log(8) + 5\log(x) \). If there was an error in the options presented, please verify.
1. The product property: \( \log(a \cdot b) = \log a + \log b \)
2. The power property: \( \log(a^b) = b \log a \)
Applying these properties to \( \log(8x^5) \):
1. Break it down using the product property:
\[
\log(8x^5) = \log(8) + \log(x^5)
\]
2. Now apply the power property to \( \log(x^5) \):
\[
\log(8x^5) = \log(8) + 5\log(x)
\]
Thus, the final expression is:
\[
\log(8) + 5\log(x)
\]
None of the provided responses match this exactly, but the correct expanded form is \( \log(8) + 5\log(x) \). If there was an error in the options presented, please verify.