Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.

Question

BlackTom AI · Accepted Answer

The problem asks to use logarithm properties to simplify the expression log base 3 of 24 minus log base 3 of 8. Start by applying the subtraction rule for logs: log_b(x) - log_b(y) = log_b(x/y). Here, b = 3, so the expression becomes log_3(24/8).

Compute the fraction inside the log: 24/8 = 3. Thus the expression simplifies to log_3(3).

Finally, since any log base b of b equals 1 (log_b(b) = 1), we have log_3(3) = 1.

Common missteps to watch for: forgetting to combine the logs into a single logarithm using the quotient rule, incorrectly dividing the numbers outside the log, or assuming log_3(3) is something other than 1 (e.g., mixing up logarithm bases or misapplying rules). The exact value is 1.

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.Numerical

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