How do you solve $8 (10^{3 x}) = 12$ $8(10^(3x))=12$ ?

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Answer 1 · 2017-02-04T15:20:25

$x = 0.0587$ $x=0.0587$ .

We will use the familiar rules of Log function.

$8 (10^{3 x}) = 12$ $8(10^(3x))=12$

$\Rightarrow 10^{3 x} = \frac{12}{8} = \frac{3}{2}$ $rArr 10^(3x)=12/8=3/2$ .

$\Rightarrow {log}_{10} 10^{3 x} = {log}_{10} (\frac{3}{2}) = {log}_{10} 3 - {log}_{10} 2$ $rArr log_10 10^(3x)=log_10 (3/2)=log_10 3- log_10 2$ .

$\Rightarrow (3 x) {log}_{10} 10 = 0.4771 - 0.3010 = 0.1761 .$ $rArr (3x)log_10 10=0.4771-0.3010=0.1761.$

$\Rightarrow 3 x = 0.1761$ $rArr 3x=0.1761$ .

$\Rightarrow x = \frac{0.1761}{3}$ $rArr x=0.1761/3$ .

$:." The Soln. is, "x=0.0587$ .

How do you solve 8(10^(3x))=128(103x)=128(10^(3x))=12?