Solve log₇5 - log₇2: Base 7 Logarithm Subtraction

Question

$\log_75-\log_72=$

00:00 Solve

00:09 We will use the formula for subtracting logarithms

00:17 Subtracting logarithms equals the logarithm of the quotient of numbers

00:24 We will use this formula in our exercise

00:34 And this is the solution to the question

To solve the problem, let's use the rules of logarithms:

Step 1: Recognize that we are dealing with the subtraction of logarithms sharing the same base, which calls for the identity $\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)$ .
Step 2: Apply this identity to the expression $\log_7 5 - \log_7 2$ .
Step 3: Realize that this can thus be expressed as a single logarithm: $\log_7 \left(\frac{5}{2}\right)$ .
Step 4: Simplify the fraction, yielding $\log_7 2.5$ .

Therefore, the simplification results in the expression: $\log_7 2.5$ .

This matches the correct answer from the given choices.

$\log_72.5$