Evaluate the given logarithm. log 7 7 0.3 \log_77^{0.3} lo g 7 7 0.3

In this problem, we're asked to evaluate the given logarithm. And here I have log base 7 of 7 to the power of 0.3. Now the first thing I notice about this log is that my base 7 is the same as what I'm taking the log of this 7 exponent to the power of 0.3. So here I can use the inverse property because I know that this log base 7 and the 7 are just going to cancel out. So I am simply left with 0.3, and we're done. Log base 7 of 7 to the power of 0.3 is just 0.3. Thanks for watching, and I'll see you in the next one.

0. Functions

Properties of Logarithms

Business Calculus

0. Functions

Properties of Logarithms

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Multiple Choice

Evaluate the given logarithm.
$\log_77^{0.3}$

$1.79$

$7$

$1$

$0.3$

Verified step by step guidance

Rewrite the logarithmic expression using the definition of a logarithm: $ \log_b(a) = c $ means $ b^c = a $. In this case, $ \log_7(7^{0.3}) $.

Simplify the expression by recognizing that the base of the logarithm (7) and the base of the exponent (7) are the same. This allows us to use the property $ \log_b(b^x) = x $.

Apply the property $ \log_7(7^{0.3}) = 0.3 $.

Verify the result conceptually: The logarithm $ \log_7(7^{0.3}) $ asks, 'To what power must 7 be raised to result in $ 7^{0.3} $?' Clearly, the answer is $ 0.3 $.

Conclude that the value of $ \log_7(7^{0.3}) $ is $ 0.3 $.