iristh3virusoo2

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 $10}^{4\mathrm{log}\left(x\right)$ , into $x}^{4$ , 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 $10}^{4\mathrm{log}\left(x\right)$ can be re-written as $10}^{4}+{10}^{\mathrm{log}\left(x\right)$ , but I'm not sure that this helps my plight! Any very basic guidance would be greatly appreciated.

mastifo5h

Beginner2022-02-24Added 6 answers

A cool rule about logarithmic functions is that

$a\cdot {\mathrm{log}}_{b}\left(x\right)={\mathrm{log}}_{b}\left({x}^{a}\right)$ .

Fron this,

$10}^{4\mathrm{log}\left(x\right)}={10}^{\mathrm{log}\left({x}^{4}\right)$ .

If we assume that you have a logarithm to the base 10, then

$10}^{{\mathrm{log}}_{10}\left({x}^{4}\right)}={x}^{4$ .

Fron this,

If we assume that you have a logarithm to the base 10, then

Radich606

Beginner2022-02-25Added 6 answers

Taking logarithms,

so you can exponentiate both sides to get to

I shall spare you the rant about using log to mean