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Simplify the expression log5(250). (Note (log(10)/(log(5) ≈ 1.4.)

Sagot :

Given the following expression:

[tex]log_5(250)[/tex]

We have given the following note:

[tex]\frac{log(10)}{log(5)}=1.4[/tex]

We will use the following rules to find the value of the given expression:

[tex]\begin{gathered} log_a(b)=\frac{log(b)}{log(a)} \\ \\ log(m^n)=n*log(m) \end{gathered}[/tex]

So, we will simplify the expression as follows:

[tex]\begin{gathered} log_5(250)=\frac{log(250)}{log(5)}=\frac{log(5^2*10)}{log(5)}=\frac{2*log(5)+log(10)}{log(5)} \\ \\ =\frac{2*log(5)}{log(5)}+\frac{log(10)}{log(5)}=2+1.4=3.4 \end{gathered}[/tex]

So, the answer will be 3.4

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