I am trying to convert part of an equation from its log form into a linear form. Specifically, I am

iristh3virusoo2

iristh3virusoo2

Answered question

2022-02-23

I am trying to convert part of an equation from its log form into a linear form. Specifically, I am trying to convert 104log(x), into x4, but I'm really unsure of how to get from this first stage to the second. My experience with logarithms and exponents is limited, though I believe that 104log(x) can be re-written as 104+10log(x), but I'm not sure that this helps my plight! Any very basic guidance would be greatly appreciated.

Answer & Explanation

mastifo5h

mastifo5h

Beginner2022-02-24Added 6 answers

A cool rule about logarithmic functions is that
alogb(x)=logb(xa).
Fron this,
104log(x)=10log(x4).
If we assume that you have a logarithm to the base 10, then
10log10(x4)=x4.
Radich606

Radich606

Beginner2022-02-25Added 6 answers

Taking logarithms,
log(104logx)=4logxlog10=logx(4log10)=log(x4log10),,
so you can exponentiate both sides to get to
104log{x}=x4log{10}.
I shall spare you the rant about using log to mean log10.

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