For the three-part question that follows identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.

Question

Use the following expression to answer the following questions. log 2 3

Part A: What is the change-of-base formula?

Part B: Name some common base choices used in the change-of-base calculation. Explain why the bases listed are common choices. Choose a base to use in simplifying the above expression.

Part C: Simplify the expression, log2 3. Round to the hundredths place.

Answer 1

Hi Ria T

Sorry but the actual question you have there log 2 3 is not showing up completely. I can’t tell if you mean

log₂3 (this reads as logarithm of 3 to the base 2) or something else.

First you need to learn the Change of Base Rule

The change of base rule works as follows: the logarithm of a to base b is equal to the ratio of the logarithm of a to base d to the logarithm of b to base d. Here d is the base of your choosing, so long as d does not equal 1.

The change of base formula is used to re-write a logarithm operation as a fraction of logarithms with a new base.

The most common use of the change of base formula is to compute logarithms on a calculator when the only logarithm operations available are ⁡ log10(⋅) and ⁡ ln or log to the base e

Change of Base Formula

d would be log = log₁₀ or ln log to the base e, the natural logarithm both are on most calculators

For log₂3 where

a = 3

b = 2

d = whatever base you decide to use

On your calculator if you chose to use base 10 that is log on your calculator while the natural is ln

log₂3 = log₁₀(3)/log₁₀(2) = log(3)/log(2) = 1.585 or 1.59 to two decimal places

I hope this helps you to get started and you can look these up on the internet or in your text.