Pre Calculus. Notes 4.4. Exponential and Logarithmic Equations (Day 1)*.
Exponential Equation: an equation in which the variable occurs in the exponent.
Ex. 1.
Pre Calculus Notes 4.4 Exponential and Logarithmic Equations (Day 1)* Exponential Equation: an equation in which the variable occurs in the exponent Ex. 1
Solve for x:
2x = 7
Steps for Solving Exponential Equations 1. Isolate the exponential expression on one side of the equation. 2. Take the log of each side, and use the Laws of Logs to bring the exponent down. 3. Solve for the variable.
Ex. Find the solution of the equation 3x+2 = 7, correct to six decimal places.
Ex. Solve the equation 8e2x = 20
1
Ex. Solve the equation e3-2x = 4 algebraically and graphically.
Ex. Solve the equation e2x - ex - 6 = 0.
Ex. Solve the equation 3xex + x2ex = 0.
2
Pre Calculus Notes 4.4 Exponential and Logarithmic Equations (Day 2) Logarithmic equation is one in which a log of the variable occurs.
log2 (x+2) = 5
Steps for Solving Logarithmic Equations 1. Isolate the log term on one side of the equation; you must first need to combine the log terms. 2. Write the equation in exponential form (or raise the base to each side of the equation.) 3. Solve for the variable.
Ex. Solve for x : ln x = 8
Ex. Solve for x: log 2 (25-x) = 3
Ex. Solve for x : 4 + 3log (2x) = 16
3
Ex. Solve the equation log (x+2) + log (x-1) = 1 both algebraically and graphically.
Ex. A sum of $5000 is invested at an interest rate of 5% per year. Find the time required for the money to double if the interest is compounded (b) continuously (a) semiannually
