Please, write the logarithm as a ratio of common logarithms

waigaK

waigaK

Answered question

2021-08-14

Please, write the logarithm as a ratio of common logarithms and natural logarithms.
log9(69)
a) common logarithms
b) natural logarithms

Answer & Explanation

SkladanH

SkladanH

Skilled2021-08-15Added 80 answers

Given, log9(69)
a) let logba=x then we know that bx=a
Now taking common log (to the base 10) on both side, we get
logbx=loga
xlogb=loga
x=logalogb
As x=logba, we can state logba=logalogb
Hence, in common
log9(69)=log69log9
b) bx=a
Taking natural logarithsm we get
lnbx=lnaxlnb=lna
x=lnalnb
In natural logarithm log9(69)=ln69ln9

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