Use the Change of Base Formula and common logs or natural logs to approximate the value of log3(45) using a calculator.

Answer 1

Hi Shayleigh,

I will use the change of base formula for logarithms to solve this program. The equation for this is as follows:

log_b(a) = log_x(a) / log_x(b)

Note that x represents the value of the logarithm base we want to use, we can use any positive value that is NOT equal to one.

Let us use x = 10 as our base, and then use a calculator to solve this equation:

log₃(45)

= log₁₀(45) / log₁₀(3)

~ 3.44

Answer 2

Natural log: log₃(45) = ln(45)/ln(3)

Common log: log₃(45) = log(45)/log(3)

Then plug on of those into the calculator and you're set!