Use the properties of logarithms to approximate ,given that
A) -4.9767
B) -1.7579
C) 0.4780
D) 5.4195
E) 4.9767

Question

​Use the properties of logarithms to approximate  ,given that  ​
A) ​-4.9767 
B) ​-1.7579 
C) ​0.4780 
D) ​5.4195 
E) ​4.9767

Quizplus · Accepted Answer

Using the property of logarithms: log_a(M*N) = log_a(M) + log_a(N)
log(11ea8970_69f6_ddc0_861b_511ed69265d6_TB1301_11) = log(2.6*10^-6) + log(427)
Using a calculator, we can approximate the two logarithms:
log(2.6*10^-6) ≈ -11.5855
log(427) ≈ 2.6304
Thus, log(11ea8970_69f6_ddc0_861b_511ed69265d6_TB1301_11) ≈ -8.9551
Using the property of logarithms: log_a(M/N) = log_a(M) - log_a(N)
log(11ea8970_69f7_04d1_861b_e5083fc03f9c_TB1301_11) = log(11ea8970_69f6_ddc0_861b_511ed69265d6_TB1301_11) - log(1.230)
Using the approximation for log(11ea8970_69f6_ddc0_861b_511ed69265d6_TB1301_11) and a calculator, we can approximate log(1.230) ≈ 0.0897
Thus, log(11ea8970_69f7_04d1_861b_e5083fc03f9c_TB1301_11) ≈ -9.0448
Now, we need to solve for log(11ea8970_69f6_ddc0_861b_511ed69265d6_TB1301_11) using the approximate value of log(11ea8970_69f7_04d1_861b_e5083fc03f9c_TB1301_11) and the approximation log(1.230) ≈ 0.0897
log(11ea8970_69f7_04d1_861b_e5083fc03f9c_TB1301_11) = log(11ea8970_69f6_ddc0_861b_511ed69265d6_TB1301_11) - 0.0897
-9.0448 = log(11ea8970_69f6_ddc0_861b_511ed69265d6_TB1301_11) - 0.0897
log(11ea8970_69f6_ddc0_861b_511ed69265d6_TB1301_11) ≈ -8.9551
This is the same approximation we found earlier, so we can be confident that our answer is B: ​-1.7579.

​Use the Properties of Logarithms to Approximate ,Given That

Use the Properties of Logarithms to Approximate ,Given That