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

3 Answers
Alvin L.
Mar 4, 2018

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

Ratnaker Mehta
Mar 4, 2018

"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.

Jim G.
Mar 4, 2018

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"

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