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Sagot :
The equation is 4^{3x} is equal to 8^{1/x} 2^{x+3} and the values of x are x is equal to (3+√69)/(10) or x is equal to (3-√69)/(10)
What is an exponential function?
It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]
where 'a' is a constant and a>1
After following the rules to model the equation.
The equation becomes:
[tex]\rm 4^3^x= 8^{1/x}\times 2^{x+3}[/tex]
After solving, we get:
[tex]2^{6x}= 2^{3/x \ +x+3}[/tex] (power rule)
Taking log on both sides with base 2
[tex]\rm log_2(2^{6x})= log_2(2^{3/x \ +x+3})[/tex]
After solving, we will get a quadratic equation:
[tex]\rm 5x^2-3x-3 = 0[/tex]
After using quadratic formula, we will get,
[tex]\rm x=\dfrac{3+\sqrt{69}}{10}[/tex] or
[tex]\rm x=\dfrac{3-\sqrt{69}}{10}[/tex]
Thus, the equation is 4^{3x} is equal to 8^{1/x} 2^{x+3} and the values of x are x is equal to (3+√69)/(10) or x is equal to (3-√69)/(10)
Learn more about the exponential function here:
brainly.com/question/11487261
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