Simplifying and Solving Exponential Expressions: Tips and Tricks

In summary, the conversation discusses how to simplify an exponential expression and solve an equation involving exponents. It is noted that the first expression cannot be simplified further, while the second equation can be solved by converting it into ordinary algebraic notation and using the laws of exponents. The conversation also briefly mentions using latex code to present mathematical equations.
  • #1
amd123
110
0
1. (3*square root of 2)^square root of 2 How do I simplify this and other exponential expressions?
2. 3^(power of 2*x)-1=3^(power of x) + 2 How do i solve this?

I don't know how to attempt it...Help please
 
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  • #2
Regarding your first question: you can't, really. Subjectively, there's no "simpler" form than what you already have.

Regarding your second question: define y=3^x, and recast your equation in terms of y. Can you solve this?
 
  • #3
according to glencoe algebra 2 number 1 can be simplified even more but they don't tell HOW?

no https://www.physicsforums.com/latex_images/16/1681321-1.png [Broken] that's what its supposed to look like, i have to find x
 
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  • #4
Try this: instead of 2^(1/2), use some variable, r, for the (1/2). Now you have
something like (3*2^r)^(2^r), convert this into ordinary algebraic notation so it is easier to understand; and then use your laws of exponents.
 
  • #5
Actually what I obtain is not much clearer. Example seems like a calculator exercise.
 
  • #6
Now, I find this:

(3^(1/2))*2^((2^(1/2))/2 )

It would look better if I had access to TEX right now.
Three to the square root of two power, multiplied by two to the [square root of two] over two power. It may read complicated, but it looks neat on my paper.
 
  • #7
symbolipoint said:
Now, I find this:

(3^(1/2))*2^((2^(1/2))/2 )

It would look better if I had access to TEX right now.

You can always use latex in your posts by typing [tex] your latex code [ /tex]. (without the space in front of the /)
 

What are exponential functions?

Exponential functions are mathematical functions that have the form f(x) = ab^x, where a and b are constants and x is the independent variable. These functions are characterized by a rapidly increasing or decreasing rate of change and are often used to model growth or decay in various natural and social phenomena.

What is the difference between exponential and linear functions?

The main difference between exponential and linear functions is the rate of change. In a linear function, the rate of change is constant, while in an exponential function, the rate of change increases or decreases at an exponential rate. Additionally, linear functions have a constant slope, while exponential functions have a varying slope.

How do you graph an exponential function?

To graph an exponential function, you first need to identify the base, a, and the initial value, b. Then, plot points by substituting different values for x in the equation f(x) = ab^x. Use these points to draw a smooth curve that represents the function. You can also use a graphing calculator or software to graph exponential functions.

What are some real-life applications of exponential functions?

Exponential functions are used in various real-life applications, including population growth, compound interest, radioactive decay, and bacterial growth. They are also commonly used in economics, biology, finance, and physics to model natural and social phenomena and make predictions.

How do you solve exponential equations?

To solve exponential equations, you can use logarithms or properties of exponents. If both sides of the equation have the same base, you can set their exponents equal to each other and solve for the variable. If the bases are different, you can use logarithms to convert the equation into a simpler form and solve for the variable.

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