evaluate algebraically for exact values:
10^(x+3) = 100
10^(x+3)=10^2
http://www.regentsprep.org/Regents/math/algtrig/ATE8/exponentialEquations.htm
To evaluate this algebraic expression and find the exact value of x, we will use logarithms. Specifically, we will use the logarithm base 10 (also known as the common logarithm) to solve for x.
Step 1: Take the logarithm of both sides of the equation.
log (10^(x+3)) = log (100)
Step 2: Use the power rule of logarithms to simplify the left side of the equation.
(x + 3) log (10) = log (100)
Step 3: Evaluate the logarithms. The common logarithm of 10 is 1, and the common logarithm of 100 is 2.
(x + 3) × 1 = 2
Step 4: Simplify the equation.
x + 3 = 2
Step 5: Solve for x.
x = 2 - 3
x = -1
So, the exact value of x that satisfies the equation 10^(x+3) = 100 is x = -1.