I cannot figure out how to work this one. I have tried working it like the example in the book but cannot come up with one of the answers given. Please help.

Use log5(2)=0.4307 and log5(3)=0.6826 to approximate the value of log5=54.

According to the book's example you would divide 0.6826 by 0.4307 which equals 1.58 (not one of the choices)

The answers are:
a) 0.1370
b) 2.4785
c) 0.8820
d) 0.7488

Thanks for your help

To solve this problem, we can use the logarithmic property that says:

log(base a) (b^c) = c * log(base a) (b)

So let's use this property to approximate log5(54).

First, note that 54 can be written as a power of 2 and 3:

54 = (2^2) * 3^3

Using the logarithmic property, we can rewrite this as:

log5(54) = log5((2^2) * 3^3)
= log5(2^2) + log5(3^3)
= 2 * log5(2) + 3 * log5(3)

Now, we can substitute the given values of log5(2) and log5(3):

log5(54) = 2 * 0.4307 + 3 * 0.6826

Multiplying the values:

log5(54) = 0.8614 + 2.0478
= 2.9092

So the approximate value of log5(54) is 2.9092.

None of the given answer choices match exactly to 2.9092. However, we can find the closest match. By comparing the given options, we can see that the closest value is 2.4785 (option b).