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7-58.
  1. Compute the value of each expression without using a calculator. Homework Help ✎

    1. log(8) + log(125)

    2. log25(125)

    3. log(25) + log(20)

    4. 7log7(12)

Use the Product Property of Logs:
log(N) + log(M) = log(NM).

log(8 · 125)

Remember you are working in log base 10.

log10(1000)

3

Think of this in exponential form.

25? = 125

Rewrite each side of the equation as a power of 5. The exponents are equal.

(52)? = 53

Apply the Power Property of Logs to the first logarithm and simplify.

log(5) + log(20)

Use the Product Property of Logs, as in part (a).

Let log7(12) = x. Therefore the original expression becomes 7x. But 7x = 12.