# Math 10

EXPONENTIAL EQUATION

Find the X

3^x - 82/9 = -3^-x

1. 👍
2. 👎
3. 👁
1. 3^x + 3^-x = 82/9
3^x + 1/3^x = 82/9
(3^2x + 1)/3^x = 82/9
clearly, x=2, but let's go on.
9(3^2x + 1) = 82*3^x
9*3^2x - 82*3^x + 9 = 0
think of this as 9u^2-82u+9, and you get
(9*3^x - 1)(3^x - 9) = 0
3^x = 9 or 1/9
x = 2 or -2
aha. an unexpected solution!

1. 👍
2. 👎
2. Thank you so much. It really helps me 😂

1. 👍
2. 👎

## Similar Questions

1. ### Exponential Growth and Decay

Can somebody please check my answers? 1. Identify the initial amount a and the growth factor b in the exponential function. g(x)=14*2^x a)a=14, b=x b)a=14, b=2

2. ### Alg 2 HELP!!

1.) Find an exponential function of the form y=ab^x whose graph passes through the points (2,48) and (5,3072) 2.) The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when

3. ### math

the population of a southern city follows the exponential law. If the population doubled in size over an 18 month period and the current population in 10000, what will be the population 2 years from now? the equation for the

4. ### am I right ? or no?

Which equations represent exponential growth? Which equations represent exponential decay? Drag the choices into the boxes to complete the table. Exponential Growth: y=4000(1.0825)^t ,y=12,000(0.72)^t , y=8000(0.97)^t ,

1. ### Algebra II

Use the equation of the exponential function whose graph passes through the points (0,-2) and (2,-50) to find the value of y when x = -2. I know the formula is y=ab^x but I don't know what numbers to plug in. Any help would be

2. ### Algebra 1- Exponential Growth & Decay

How are exponential growth and decay present in the real world? Give at least 2 examples for exponential growth and 2 examples of exponential decay. My Answer: I have only been able to think of one example of exponential growth

3. ### Algebra

a. Do some research and find a city that has experienced population growth. Determine its population on January 1st of a certain year. Write an exponential function to represent the city’s population, y, based on the number of

4. ### Algebra

Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is

1. ### Exponential Functions

Hello! How would I prove that the data is exponential? I tried to find a pattern but was unsuccessful. Here is the question: Prove that the data is exponential. Data: x y 0 7 1 8 2 9 3 10 4 11 5 13 6 14 7 16 8 18 9 21 10 23 11 26

2. ### Mathematics

. The three consecutive terms of an exponential sequence (G.P) are the second, third and sixth terms of a linear sequence (A.P). Find the common ratio of the exponential sequence.

3. ### College Algebra

1. Find the domain of the composite function f o g. f(x)= 2/x-3; g(x)= 7/x 2. Solve the following exponential equation. Exact answers only. 2^1-9x = e^2x

4. ### algebra

log9 1= _______ (fill in the blank) Let x=log2 1/32 . Write the exponential form of the equation and solve the equation for x.