How do you evaluate $log_9 0.4$ using the change of base formula?

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Answer 1 · 2018-04-17T20:13:45

$log_9(0.4)=ln(0.4)/ln(9)~~-0.4170218835$

for:

$y=log_9(0.4)<=>9^y=0.4$

$9^y=0.4$

Taking natural logarithms of both sides:

$yln(9)=ln(0.4)$

Dividing by $ln(9)$

$y=ln(0.4)/ln(9)$

But:

$y=log_9(0.4)$

$:.$

$log_9(0.4)=ln(0.4)/ln(9)$

This is the change of base formula.

$log_9(0.4)=ln(0.4)/ln(9)~~-0.4170218835$

How do you evaluate log_9 0.4log_9 0.4 using the change of base formula?