Question

2^3x = 8^4x+3
how is it equal
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Answer 1

answer

2^3x=8^4x+3

2^3x=2^12x+9

equating

3x=12x+9

3x-12x=9

-9x=9

x=-1

Answer 2

Answer:

x = - 0.176 .

Step-by-step explanation:

Given :

$\displaystyle{2^{3x}=8^{4x}+3}$

Rewrite as :

$\displaystyle{2^{3x}=2^{3\times4x}+3}\\\\\displaystyle{2^{3x}=2^{12x}+3}$

Taking log both side ;

$\displaystyle{\log2^{3x}=\log(2^{12x}+3)}\\\\\displaystyle{\log2^{3x}=\log2^{12x}+\log3}$

3 x log 2 = 12 x log 2 + log 3

12 x log 2 - 3 x log + log 3 = 0

9 x log 2 + log 3 = 0

We know value of :

log 2 = 0.3010  & log 3 = 0.4771

9 x ( 0.3010 ) + 0.4771 = 0

2.709 x = - 0.4771

x = - 0.176 .