Use $\log _ { 36 } 6 = 0.5000$ , $\log _ { 36 } 2 \approx 0.1934$ , and the properties of logarithms to approximate $\log _ { 36 } 12$ to four decimal places. Do not use a calculator.
A) $4.1589$
B) $0.3869$
C) $0.6934$
D) $3.5835$
E) $1.2420$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, $\log_{36} 12 = \log_{36} (6 \times 2) = \log_{36} 6 + \log_{36} 2 = 0.5000 + 0.1934 = 0.6934$.

Use log⁡366=0.5000\log _ { 36 } 6 = 0.5000log36​6=0.5000 log⁡362≈0.1934\log _ { 36 } 2 \approx 0.1934log36​2≈0.1934

Use $\log _ { 36 } 6 = 0.5000$ $\log _ { 36 } 2 \approx 0.1934$