Answered

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Express as a product.

[tex]\[ \ln \sqrt[6]{5} \][/tex]
[tex]\[ \ln \sqrt[6]{5} = \][/tex]

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Sagot :

GinnyAnswer
To express [tex]\( \ln \sqrt[6]{5} \)[/tex] as a product and simplify the expression, follow these steps:

1. Rewrite the expression inside the natural logarithm:

The sixth root of [tex]\( 5 \)[/tex] can be written as [tex]\( 5^{1/6} \)[/tex]. Therefore, we have:
[tex]\[ \ln \sqrt[6]{5} = \ln (5^{1/6}) \][/tex]

2. Use the logarithm power rule:

The power rule for logarithms states that [tex]\( \ln (a^b) = b \cdot \ln (a) \)[/tex]. Applying this rule, we get:
[tex]\[ \ln (5^{1/6}) = \frac{1}{6} \cdot \ln 5 \][/tex]

So, the expression [tex]\( \ln \sqrt[6]{5} \)[/tex] can be simplified and expressed as:
[tex]\[ \ln \sqrt[6]{5} = \frac{1}{6} \cdot \ln 5 \][/tex]

This is the final simplified form.
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