QuestionUse properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. $\ln \sqrt[15]{x}$

Studdy Solution

STEP 1

1. We are given a logarithmic expression involving a radical.
2. We can use properties of logarithms to simplify and expand the expression.
3. The expression can be rewritten using the power rule for logarithms.

STEP 2

1. Rewrite the radical expression in exponential form.
2. Apply the power rule for logarithms to expand the expression.

STEP 3

Rewrite the radical expression $\sqrt[15]{x}$ in exponential form.
The expression $\sqrt[15]{x}$ can be written as $x^{1/15}$ .

STEP 4

Apply the power rule for logarithms, which states that $\ln(a^b) = b \cdot \ln(a)$ .
Using this rule, we have:
$\ln(x^{1/15}) = \frac{1}{15} \cdot \ln(x)$
The expanded form of the logarithmic expression is:
$\frac{1}{15} \ln(x)$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms