Answer: assuming that this was your equation;
[tex]\frac{1}{16} =64^{4x-3}[/tex]
You answer is x= 7/12
Step-by-step explanation:
First, rewrite 1/16 as 2^-4 and 64^4x-3 as 2^24x-18
This will leave you with;[tex]2^{-4} =2^{24x-18}[/tex]
Since bases are the same, set the exponents equal (eliminate the 2’s);
-4=24x-18
Move 24x to the left to get; -24x-4=-18
Move constant to the right to get -24x=-18+4
Add 4 to -18 to get; -24x=-14
Divide both sides by -24 to get you final answer for x which is 7/12
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The required value of exponential equation is x = [tex]\frac{7}{12}[/tex].
Given that,
Exponential equation; [tex]\frac{1}{16} = 64^{4x-3}[/tex]
We have to determine,
The value of x.
According to the question,
To obtain the value of x by solving the exponential equation follow all the steps given below.
Exponential equation;
[tex]\dfrac{1}{16} = 64^{4x-3}[/tex]
Then,
[tex]\dfrac{1}{16} = 64^{4x-3}\\\\\dfrac{1}{2^{4}} = 2^{6(4x-3)}\\\\2^{-4} = 2^{24x-18}\\\\[/tex]
Since, bases are the same, set the exponents equation,
Then,
Equating the power of exponential equation,
[tex]-4 = 24x-18\\\\24x = -4+18\\\\24x = 14\\\\x = \dfrac{14}{24}\\\\x = \dfrac{7}{12}[/tex]
Hence, The required value of exponential equation is [tex]\frac{7}{12}[/tex].
To know more about Exponential function click the link given below.
https://brainly.com/question/20912064
