Solving Exponential and Logarithmic Equations

To solve 5(2^x + 4) = 15, first divide each side by

5

An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e0.05t = 150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use your calculator and round to the nearest whole number.

8 years

What equation is equivalent to 9^x - 3 = 729?

9^x - 3 = 9^3

What is the solution to ln (x2 - 16) = 0?

A.

Find the solutions to the equation 10^2x + 11 = (x + 6)^2 - 2. Which values are approximate solutions to the equation? Select two answers.

A. -9.6 D. -2.4

Select all of the potential solution(s) of the equation 2log5x = log54.

A. x=-2 E. x=2

To solve e^4 - 3x = 4/3x + 9 by graphing, which equations should be graphed?

B, E

Which equation is equivalent tolog5x3 - logx2 = 2?

B.

What are the potential solutions oflog6x + log6(x + 5) = 2?

B. -9 C. 4

Which equation is equivalent tolog4 + log(x + 2) = 1?

B. 4x + 8 = 10^1

Solve: e^2x + 5 = 4

C.

Solve 2 + 3e^x + 2 = 7 for x.

C. x=In(5/3)-2

Which of the following is the solution of 5e^2x - 4 = 11?

C. x=In3/2

Which are possible first steps in solving the equation 4^x + 3 = 18?

C.Take the base-4 logarithm of each side. D. Take the natural logarithm of each side. E. Take the common logarithm of each side.

Use the given graph to determine if there are any solutions to the equation −(5)^3 − x + 4 = −2x.

The solution is approximately 1.7 because it is the x-value of the intersection of the functions.

Consider the equation log(3x - 1) = log28. Explain why 3x - 1 is not equal to 8. Describe the steps you would take to solve the equation, and state what 3x - 1 is equal to.

Which did you include in your answer? -The bases are not the same, so you cannot set 3x - 1 equal to 8. -You can evaluate the logarithm on the right side of the equation to get 3. -You can use the definition of a logarithm to write 3x - 1 = 1000.

To solve the equation 2x - 1 - 7 = 9,first

add 7 to each side

Consider 8^x-4 = 8^10 Because the ___ are equal, the ___ must also be equal The solution to the equation is

bases & exponents x=14

A computer was originally purchased for $900 and undergoes a 14% annual depreciation rate. The computer is now worth $364. The number of years that have passed, t, since the computer was purchased can be found using the following equation: 364 = 900(1 − 0.14)^t Solve the equation by graphing to determine how many years have passed since the computer was purchased. Round to the nearest whole year.

t=6 years

What is the solution to the equation 4(1/2)^x-1= 5x+2? Round to the nearest tenth.

0.6

What common base can be used to rewrite each side of the resulting equation?

2

Which is the equation of 2x - 1 - 7 = 9 after it is reduced so that both sides of the equation are exponential functions with the same base?

2^x-1=2^4

Which graph shows the solution to the equation 4x - 3 = 8?

3rd option

What is the solution oflog6x + log6(x + 5) = 2?

4

The solution of the equation 2x - 1 - 7 = 9is

x = 5

Solve 4x - 3 = 18. Round to the nearest thousandth.

x = 5.085

Complete the steps to solve the equation 4e2 + 2x = x − 3 by graphing. 1) Write a system of equations. y = 4e^2 + 2x and y = ___ 2) Graph the system. Use the graphing calculator to graph each equation. 3) Identify the solutions. The ___ of the points where the graphs of the equations intersect are the solutions to the original equation. The equation 4e2 + 2x = x - 3 has

x-3 x-coordinates no solution

The solution to the equation is

x= 1/2

Solve 5(2^x + 4) = 15. Round to the nearest thousandth.

x=-2.415

Solve -(6)^x-1 + 5=(2/3)^2-x by graphing. Round to the nearest tenth.

x=1.8

Solve: ln 2x + ln 2 = 0

x=1/4

What is the solution to2log5x = log54?

x=2

Solve: log5x3 - logx2 = 2

x=20

Solve: 9^x - 3 = 729

x=6