Answer:
x=7/5
Step-by-step explanation:
We can write it in exponential form
128= 2^2*2x * 2^x
2^4x+x=5x
2^5x=128
2^5x=2^7
5x=7
x=7/5
The value of x in the equation given is
[tex] \frac{7}{5} [/tex]
To solve :
[tex]128 = {4}^{2x} \times {2}^{x} [/tex]
Change all values to have the same root :
[tex] {2}^{7} = {2}^{2(2x)} \times {2}^{x} [/tex]
[tex] {2}^{7} = {2}^{4x} \times {2}^{x} [/tex]
[tex] {2}^{7} = {2}^{(4x + x)} [/tex]
[tex] {2}^{7} = {2}^{5x} [/tex]
The roots cancel out
[tex] 7 = 5x[/tex]
Divide both sides by 5
[tex]x = \frac{7}{5} [/tex]
Therefore, the value of
[tex]x = \frac{7}{5} [/tex]
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