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Jobisdone [24]
2 years ago
11

(Evaluate each logarithm. Use the change of base formula when necessary) helpppp y’all

Mathematics
1 answer:
Dmitry [639]2 years ago
5 0

The value of \log _{6}(36) is 2.

Solution:

Given expression is \log _{6}(36).

<u>To evaluate the expression:</u>

\log _{6}(36)

36 can be written as 6².

       =\log _{6}\left(6^{2}\right)

Using log rule: \log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)

       =2 \log _{6}(6)

Using log rule: \log _{a}(a)=1 so that \log _{6}(6)=1

       = 2(1)

       = 2

\log _{6}(36)=2

Hence the value of \log _{6}(36) is 2.

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Step-by-step explanation:

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1) First, distribute the numbers outside of the set of parentheses to the terms inside the set of parentheses next to them. Then, simplify the fractions.

3(\frac{7}{5} x + 4) -2 (\frac{3}{2} -\frac{5}{4} x)

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2) Finally, combine like terms. (This means to add or subtract constants and to add or subtract terms with the same variables.) You may need to convert terms to the same denominator in order to do so easier. Then, reduce the fraction.

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