Question

Find the value of each logarithm using the change of base formula.

Answer 1

\[\log _{0.5}0.0675\]

Answer 2

the change of base formula uses base e or base 10 logs

the general form below uses base e logs

\[\log_{a}(b) = \frac{\ln(b)}{\ln(a)}\]

so in your question a = 0.5 and b = 0.0675

just substitute and evalaute

Answer 3

log 0.0675/ log 0.5 , = 3.88 ?

Answer 4

not quite try

\[\frac{\ln(0.0675)}{\ln(0.5)}\]

Answer 5

I used base e you have used base 10.... they will result in the same answer..

Answer 6

or you could use

\[\frac{\log_{10}(0.0675)}{\log_{10}(0.5)}\]

Answer 7

oops my mistake... your answer is correct... sorry about that

Answer 8

so 3.88 ?

Answer 9

I have 3.88897

so to 2 decimal places its 3.89

Answer 10

yes