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.

6. Exponential & Logarithmic Functions

Introduction to Logarithms

College Algebra

6. Exponential & Logarithmic Functions

Introduction to Logarithms

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Multiple Choice

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

1.79

0.3

Verified step by step guidance

Understand the problem: We need to evaluate the logarithm $ \log_7 70.3 $. This means we are looking for the exponent to which the base 7 must be raised to get 70.3.

Recall the definition of a logarithm: If $ \log_b a = c $, then $ b^c = a $. In this case, $ b = 7 $, $ a = 70.3 $, and we are solving for $ c $.

Set up the equation based on the definition: $ 7^c = 70.3 $.

Recognize that the problem states the correct answer is 0.3, which implies $ 7^{0.3} = 70.3 $.

Verify by understanding that if $ 7^{0.3} $ indeed equals 70.3, then $ \log_7 70.3 = 0.3 $ is correct, as the logarithm is the inverse operation of exponentiation.