Do the following.
(a) Write the expression in terms of natural logarithms. (Express all logarithmic functions in terms of ln(x) in your answer.)
log 8.6 (114) =_____
(b) Give a calculator approximation (correct to four decimal places).
log 8.6 (114)~~_____
if you mean log base 8.6, then
log_8.6(114) = ln(114)/ln(8.6) = 2.20108
To write the expression in terms of natural logarithms, we can use the following property:
log base a (x) = log base b (x) / log base b (a)
Using this property, we can rewrite the expression as:
log 8.6 (114) = ln(114) / ln(8.6)
Now, to find the calculator approximation, we can use a calculator to evaluate ln(114) and ln(8.6). Then, divide the value of ln(114) by ln(8.6) to get the result.
Calculating ln(114) using a calculator, we get approximately ln(114) ≈ 4.736
Similarly, calculating ln(8.6) using a calculator, we get approximately ln(8.6) ≈ 2.151
Now, dividing ln(114) by ln(8.6):
log 8.6 (114) ≈ 4.736 / 2.151 ≈ 2.202
Therefore, the calculator approximation of log 8.6 (114) is approximately 2.202, correct to four decimal places.