Question

4 в степени x = 8 2 в степени x = 1/8

Answer 1

${4}^{x} = 8 \\ {2}^{2x} = {2}^{3} \\ 2x = 3 \\ x = \frac{3}{2} \\ x = 1.5$

${2}^{x} = \frac{1}{8} \\ {2}^{x} = {2}^{ - 3} \\ x = - 3$

Answer 2

To solve the equations, we need to find the value of 'x' in each equation. Let's start by solving each equation step by step:

1. $4^x = 8$

To solve this equation, we need to find the value of 'x' such that $4$ raised to the power of 'x' equals $8$.

First, we notice that $8$ can be expressed as $2^3$. So, we can rewrite the equation as:

$4^x = 2^3$

Now, since both sides have a base of 2, we can equate the exponents:

$x = 3$

So, the solution to the first equation is $x = 3$.

2. $2^x = \frac{1}{8}$

To solve this equation, we rewrite $1/8$ as $2^{-3}$ (since $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$):

$2^x = 2^{-3}$

Again, since both sides have a base of 2, we can equate the exponents:

$x = -3$

So, the solution to the second equation is $x = -3$.

In summary:

1. $4^x = 8$ has a solution $x = 3$.
2. $2^x = \frac{1}{8}$ has a solution $x = -3$.