Evaluate the logarithm log₇ 126 using the change of base formula.Round to 3 decimal places. A)4.836 B)2.485 C)0.402 D)9.411 E)2.1

Question

Quizplus · Accepted Answer

Using the change of base formula:
logS1U1B17S1U1B0 126 = log(126)/log(S1U1B17S1U1B0)
Then, calculating the denominator:
log(S1U1B17S1U1B0) = log(S1U1B17) + log(S1U1B0)
Using the rules of logarithms,
log(S1U1B17S1U1B0) = log(S1U1B17) + log(1) = log(S1U1B17) = log(17)/log(S1U1B)
Plugging everything in, we get:
log(126)/log(S1U1B17S1U1B0) ≈ log(126)/(log(17)/log(S1U1B)) ≈ 2.485 (rounded to 3 decimal places). Therefore, the answer is B.

Evaluate the Logarithm Log7 126 Using the Change of Base

Evaluate the Logarithm Log₇ 126 Using the Change of Base