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

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

Understand the problem: We need to evaluate the logarithm $ \log_7 7^{0.3} $. This is a logarithmic expression where the base is 7 and the argument is $ 7^{0.3} $.

Recall the logarithmic identity: $ \log_b b^x = x $. This identity states that the logarithm of a base raised to an exponent is equal to the exponent itself.

Apply the identity: In our problem, the base $ b $ is 7, and the exponent $ x $ is 0.3. Therefore, using the identity, $ \log_7 7^{0.3} = 0.3 $.

Verify the solution: Check that the application of the identity is correct by considering the definition of logarithms. The logarithm $ \log_b a $ is the power to which the base $ b $ must be raised to obtain $ a $. Here, $ 7^{0.3} $ is indeed the result of raising 7 to the power of 0.3.

Conclude: The value of the logarithm $ \log_7 7^{0.3} $ is 0.3, as expected from the identity and verification.