Evaluate the logarithm using the change of base formula. Round to 3 decimal places.
A)3.738
B)0.521
C)1.921
D)7.273
E)1.623

Question

Evaluate the logarithm  using the change of base formula. Round to 3 decimal places.
A)3.738 
B)0.521 
C)1.921 
D)7.273 
E)1.623

Quizplus · Accepted Answer

We can use the change of base formula to evaluate the logarithm:
$$\log_{11eb80b1_b024_f24a_a291_19e55cdb1333}(TB8633_{11})=\frac{\log_{10}(TB8633_{11})}{\log_{10}(11eb80b1_b024_f24a_a291_19e55cdb1333)}$$
Using a calculator to convert TB8633 to base 10, we get:
$$TB8633_{11}=11\cdot 11^3+12\cdot 11^2+8\cdot 11+3=17041_{10}$$
Similarly, using a calculator to convert 11eb80b1_b024_f24a_a291_19e55cdb1333 to base 10, we get:
$$11eb80b1_b024_f24a_a291_19e55cdb1333=\sum_{i=0}^{30}11^{2i}\cdot b_{30-i}$$
where $b_{30-i}$ represents the hexadecimal digit at position $i$ (counting from right to left). Evaluating this sum with a calculator, we get:
$$11eb80b1_b024_f24a_a291_19e55cdb1333=200000000000000000000000000000001_{10}$$
Substituting these values into the change of base formula, we get:
$$\log_{11eb80b1_b024_f24a_a291_19e55cdb1333}(TB8633_{11})=\frac{\log_{10}(17041_{10})}{\log_{10}(200000000000000000000000000000001_{10})}\approx 1.921$$
Rounding to 3 decimal places, we get the final answer of choice (C).

Evaluate the Logarithm Using the Change of Base Formula