Question

16^2x =1/128 . find x​

Answer 1

Answer:

The value of x is -7/8.

Step-by-step explanation:

GIVEN DATA

The given equation is $16^{2x} =\frac{1}{128}$

TO DETERMINE

To calculate x.

EVALUATION

The expression on the right-hand side of the equation can first be made simpler:

We can write 128 as powers of 2.

128 = $2^{7}$

So, $\frac{1}{128}= \frac{1}{2^{7} } = 2^{-7}$

Similarly, we can simplify the expression on the left-hand side:

$16^{2x} = 2^{4\times 2x} = 2^{8x}$

Now we can substitute these simplified expressions back into the original equation and solve for x:

So, the given expression $16^{2x} =\frac{1}{128}$ can be written as

$2^{8x} =2^{-7}$

Since the base is the same, we can equate the powers,

So, we have

8x = -7

x = -7/8

Therefore, the value of x is -7/8.

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