Sure, let's solve the problem step by step.

We need to find the value of $ \log_5 \sqrt[4]{5} $.

Step 1: Express the fourth root in exponential form.
$$ \sqrt[4]{5} = 5^{1/4} $$

Step 2: Substitute this into the logarithm.
$$ \log_5 (5^{1/4}) $$

Step 3: Use the logarithm power rule, which states $ \log_b (a^c) = c \log_b (a) $.
$$ \log_5 (5^{1/4}) = \frac{1}{4} \log_5 (5) $$

Step 4: Simplify using the fact that $ \log_b (b) = 1 $.
$$ \log_5 (5) = 1 $$

Step 5: Substitute back into the equation.
$$ \frac{1}{4} \log_5 (5) = \frac{1}{4} \times 1 = \frac{1}{4} $$

So, the value of $ \log_5 \sqrt[4]{5} $ is $ \frac{1}{4} $.

Question

Sure, let's solve the problem step by step.

We need to find the value of $ \log_5 \sqrt[4]{5} $.

Step 1: Express the fourth root in exponential form.
$$ \sqrt[4]{5} = 5^{1/4} $$

Step 2: Substitute this into the logarithm.
$$ \log_5 (5^{1/4}) $$

Step 3: Use the logarithm power rule, which states $ \log_b (a^c) = c \log_b (a) $.
$$ \log_5 (5^{1/4}) = \frac{1}{4} \log_5 (5) $$

Step 4: Simplify using the fact that $ \log_b (b) = 1 $.
$$ \log_5 (5) = 1 $$

Step 5: Substitute back into the equation.
$$ \frac{1}{4} \log_5 (5) = \frac{1}{4} \times 1 = \frac{1}{4} $$

So, the value of $ \log_5 \sqrt[4]{5} $ is $ \frac{1}{4} $.

Knowee AI · Accepted Answer