Question

32^x-2 = 64 + 8^x. find x​

Answer 1

0.8 is ans
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Answer 2

Answer:

Concept:

Power Rule of Exponent:

• The Exponent Power Rule states that you must multiply the exponent by the power in order to raise a number with an exponent.

• The exponent power rule's formula is $( x^{p} )^q = x^{p*q}$

Given:

The given expression is $32^{x - 2} = 64 + 8^{x}$

To Find:

We need to find the value of $x$.

Solution:

We need to simplify the given expression,

$32^{x-2} = 64 + 8^{x}$

$(2^5)^{x-2} = 64 + (2^3)^{x}$

$2^{5*(x-2) }= 64 + (2^{3x})$

$2^{5x-10}= 2^6 + (2^{3x})$

$2^{5x-10}= 2^{6+3x}$

By Comparing powers,

${5x-10} = {6+3x}$

$5x - 3x = 6 +10$

$2x = 16$

$x = \frac{16}{2}$

$x = 8$

Therefore, The value of x is $8$.

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