Question

8^x=64/2^x find the value of x​

Answer 1

Answer:

$\frac{3}{2}$ is the required value of x

Step-by-step explanation:

Explanation:

Given that, $8^x = \frac{64 }{2^x}$

• $(a^m)^n$ = $a^{mn}$ is the power rule for exponents. Multiply the exponent by the power to raise a number with an exponent to that power.

• We employ the same procedures for multiplying exponents with variables as we would for numbers.

Step 1:

From the question we have, $8^x = \frac{64 }{2^x}$.

This can be written as, $2^{3x} = \frac{2^6}{2^x}$

Subtracting the provided powers is the fundamental rule for dividing exponents with the same base.

⇒ $2^{3x} = 2^6 . 2^{-x}$

⇒ $2^{3x} = 2^{6 -x}$

Now, we compare both the side,

⇒ 3x = 6 - x

⇒4x = 6

⇒ x = $\frac{6}{4}$ = $\frac{3}{2}$.

Final answer:

Hence, $\frac{3}{2}$ is the required value of x.

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Answer 2

The value of x is 1.5 .

Step-by-step explanation:

• If a variable's maximum power is always 1, an equation is said to be linear. As a one-degree equation, it also goes by that name. An equation with one variable that has the usual form Ax + B = 0 is a linear equation. A coefficient, B is constant, and x is a variable in this situation. An equation with two variables that has the usual form Ax + By = C is a linear equation. A and B are coefficients, C is a constant, and the variables in this equation are x and y.

• According to the given information, The equation given here is,

$8^{x} = \frac{64}{2^{x} }$

Cross multiplying, we get,

$8^{x} * 2^{x} = 64$

Or, $(2^{3} )^{x} * 2^{x} = 64$

Or, $(2)^{3x} * 2^{x} = 64$

Or, $2^{3x + x} = 2^{6}$

Or, $2^{4x} = 2^{6}$

Comparing the powers on both sides of the equation, we get,

4x = 6

Or, x = $\frac{6}{4}$ = $\frac{3}{2} = 1.5$

Thus, the value of x is 1.5 .

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