1) Simplify the expression (2^3)^2.
Solution:
First, we have to simplify the exponent within the parentheses.
(2^3)^2 = (8)^2 = 64
So, the simplified expression is 64.
2) Simplify the expression 3^2 - 2^2.
Solution:
To simplify the expression, we need to calculate each exponent first.
3^2 = 3 * 3 = 9
2^2 = 2 * 2 = 4
Now, we subtract the two values:
9 - 4 = 5
So, the simplified expression is 5.
3) Solve the equation 4^x = 64.
Solution:
To solve for x, we need to find the exponent that will result in 64 when raised to the base of 4.
4^x = 64
Taking the logarithm of both sides of the equation will help us solve for x:
log(4^x) = log(64)
We can use the logarithmic property log(a^b) = b*log(a) to simplify the equation further:
x * log(4) = log(64)
Now, we need to substitute the values:
x * 0.60206 = 1.80618
Dividing both sides of the equation by 0.60206 will give us the value of x:
x = 1.80618 / 0.60206
x ≈ 3
So, the solution to the equation is x = 3.
Learning Target Problems #1
Accelerated 2 - Unit 4: Expressions and Equations with Exponents
1 answer