Solutions to Exponential and Logarithmic Equations
Before we go through solving exponential and logarithmic functions, let’s work on figuring out if a possible solution works in a function. Suppose you are given the function 10x = 3588 and a possible solution of x = 3.5548. How do you check to see if this solution is correct? Substitute x = 3.5548 to see if it works in the equation. The solution 3.5548 is just an approximation that has been rounded since the full answer has quite a few decimal places.
10x = 3588
103.5548 ≈ 3587.6 which is a good approximation of 3588.
If you are given the equation log(-3m – 1) = log(-4m – 6) and a possible solution of m = -5, how would you check if this solution is correct? Again, to check if m = -5 is the solution we can use the substitution property.
Since the left and right hand sides of the equations are equal, m = -5 is the solution to this equation.log(-3(-5) – 1) = log(-4(-5) – 6)
log(15 – 1) = log(20 – 6)
log14 = log14
