Answered

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128= 4^2x times 2^x
What is x?

Sagot :

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

fichoh

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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