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.

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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&#039;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&#039;m not sure that this helps my plight! Any very basic guidance would be greatly appreciated.

mastifo5h · Accepted Answer

A cool rule about logarithmic functions is that  a⋅logb(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 · Accepted Answer

Taking logarithms, log⁡(104log⁡x)=4log⁡xlog⁡10=log⁡x(4log⁡10)=log⁡(x4log⁡10),, 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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