Use the Change of Base Formula and common logs or natural logs to approximate the value of log3(4/5) using a calculator.

Answer 1

log base 3 of (4/5) = log base 3 of 4 - log base 3 of 5

log base 3 of 4 = log4/log3 with "log" as the common log, to base 10

log4/log3 = .602/.477 = 1.26 rounded off

log base 3 of 5 = log5/log3 = .6989/.473 = 1.47

1.26-1.47 = -0.21

Answer 2

First let's use a property of logarithms which takes division on the inside to subtraction on the outside. So log₃(4/5) = log₃(4) - log₃(5).

Now, as the problem states, we should use the change of base formula: log_a(x) = log_b(x)/log_b(a). This will allow us to convert to problem into a form that is more easily plugged into a calculator. (Some modern calculators can handle logarithms with any base, but less sophisticated ones typically only handle log₁₀ and ln.)

So we obtain log₃(4/5) = log₃(4) - log₃(5) = ln(4)/ln(3) - ln(5)/ln(3). Plugging this into the calculator we get about -0.203 .