Question

How do you use the Change of Base Formula and a calculator to evaluate the logarithm `log_5 7`?

Answer 1

`log_5(7)~~1.21`

Explanation:

The change of base formula says that:
`log_alpha(x)=log_beta(x)/log_beta(alpha)`

In this case, I will switch the base from `5` to `e`, since `log_e` (or more commonly `ln`) is present on most calculators. Using the formula, we get:

`log_5(7)=ln(7)/ln(5)`

Plugging this into a calculator, we get:

`log_5(7)~~1.21`

Answer 2

`"Approx. "1.209`.

Explanation:

The Change of Base Formula : `log_ba=log_c a/log_c b`.

`:. log_5 7=log_10 7/log_10 5`,

`=0.8451/0.6990~~1.209`.

Answer 3

`log_5 7~~1.21" to 2 dec. places"`

Explanation:

`"the "color(blue)"change of base formula"` is.

`•color(white)(x)log_b x=(log_c x)/(log_c b)`

`"log to base 10 just log and log to base e just ln"`
`"are both available on a calculator so either will"`
`"give the result"`

`rArrlog_5 7=(log7)/(log5)~~1.21" to 2 dec. places"`

`"you should check using ln"`