find the value of x in the exponent below.
4(2^x)=8^x
since 8 = 2^3, you have
2^2 * 2^x = 2^(3x)
2^(2+x) = 2^(3x)
2+x = 3x
x = 1
check:
4(2^1) = 8^1
4*2 = 8
yep
thanks very much
To find the value of x in the exponent equation 4(2^x) = 8^x, we can simplify the equation by using exponent rules.
First, let's simplify the right side of the equation. Rewrite 8 as a power of 2: 8 = 2^3. Substituting this in the equation, we get:
4(2^x) = (2^3)^x
Next, apply the exponent rule of raising a power to another power. This rule states that (a^m)^n = a^(m*n). Applying it to our equation, we have:
4(2^x) = 2^(3x)
Now, we can equate the bases of the two sides of the equation: 2^x = 2^(3x).
For the bases to be equal, the exponents must be equal. Therefore, we can write:
x = 3x
To solve for x, we can subtract 3x from both sides:
x - 3x = 0
This simplifies to:
-2x = 0
Finally, we can solve for x by dividing both sides by -2:
x = 0
So, the value of x that satisfies the equation 4(2^x) = 8^x is x = 0.