Answer:
x = log(6480)/log(24)
Explanation:
You want the solution to the equation 2^(3x-4) = 5(3^(-x+4)).
One base
We can write the equation using one exponential term like this:
2^(3x)·2^(-4) = 5·3^(-x)·3^4
(2^3)^x/16 = 5·81/3^x
(8^x)(3^x) = 16·5·81
24^x = 6480
Logs
Taking logarithms, we have ...
x·log(24) = log(6480)
x = log(6480)/log(24)
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Additional comment
The numerical value of x is about 2.76158814729.
The relevant rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
(a^b)^c = a^(bc)
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