Evaluate a Log in terms of another Log | Solving Logarithmic Problem with Logarithmic Properties

🔴Evaluate a Log in terms of another Log | Solving Logarithmic Problem with Logarithmic Properties | if-then logarithmic problem

Hey there.

In this video, we want to solve an if-then question, where we are given that

log 27 with base 12 = a.

and we want to find the value of

log 16 with base 6 in terms of a.

We are gonna use some of the very powerful logarithmic properties in order to evaluate a log in terms of another log.

I hope you find this video helpful and enjoy watching it.

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topics covered in this video:
how to solve the if-then question
logarithmic properties
how to use log properties
how to evaluate a logarithmic expression
how to evaluate a log in terms of another log
simplifying log
change of base formula
power property of logarit

#logproperties #logarithm

[mohammad.t]

Another perfect video from you
Well done man ❤️❤️

[ssa]

Рациональный способ:
log16=4log2 по основанию 6. (1)
По основанию 12
log27=log27/log12=
=по основанию 6
=3log3/(log6+log2)=
=3log(6/2)/(1+log2)=
=3(log6-log2)/(1+log2)=
=3(1-log2)/(1+log2).
Итак, 3(1-log2)/(1+log2)=a =>
3-3log2=a+alog2;
3-a=3log2+alog2;
3-a=(3+a)log2;
log2=(3-a)/(3+a). (2)
Из (1) и (2) => log16=4(3-a)/(3+a).
Ответ: 4(3-a)/(3+a).