How do you solve $4 (1 + 10^{5 x}) = 9$ $4(1 + 10^(5x) ) = 9$ ?

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How do you solve $4 (1 + 10^{5 x}) = 9$ $4(1 + 10^(5x) ) = 9$ ?

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Answer 1 · 2016-02-09T21:21:51

I found: $x = 0.0194$ $x=0.0194$

Explanation:

Let us try to arrange it:
$1 + 10^{5 x} = \frac{9}{4}$ $1+10^(5x)=9/4$
$10^{5 x} = \frac{9}{4} - 1$ $10^(5x)=9/4-1$
$10^{5 x} = \frac{9 - 4}{4}$ $10^(5x)=(9-4)/4$
$10^{5 x} = \frac{5}{4}$ $10^(5x)=5/4$
let us take the log in base $10$ $10$ of both sides:
${log}_{10} [10^{5 x}] = {log}_{10} [\frac{5}{4}]$ $log_(10)[10^(5x)]=log_(10)[5/4]$
giving:
$5 x = {log}_{10} [\frac{5}{4}]$ $5x=log_(10)[5/4]$
and:
$x = \frac{{log}_{10} [\frac{5}{4}]}{5} = 0.0194$ $x=(log_(10)[5/4])/5=0.0194$

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How do you solve $4 (1 + 10^{5 x}) = 9$ $4(1 + 10^(5x) ) = 9$ ?

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