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1. Just take a root. ex x3= 216
x = cube root 216
x = 6
2. Factoring if possible. ex x2 + 4x - 5 = 0
(x+5)(x-1)= 0
x = -5 and x = 1
3. other types of these require lots of guided guessing from andanced math courses.
4. the exponent is the variable. use logarithms
ex 3x = 5
x ln3 = ln 5
x = (ln 5)/(ln 3)
OF COURSE some alg might need to be used to rearrange the equations to get them to look like the examples.
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How do you solve a problem that has a variable with an exponent?
multiply
How can you solve this problem 100t-16t exponent 2 equals 0?
100t -16t2 = 0 t4(25-4t) = 0 t = 0 or t = 25/4
What if the problem is a fraction with a negative exponent?
Flip the fraction top-to-bottom, and delete the minus sign from the exponent.
What is the operation of logarithms?
The power operation, for example: x = 210 (answer: x = 1024) has two inverse operations, depending which of the two numbers you have to solve for. To solve for the base if you know the exponent is called calculating the root. For example: x10 = 1024 This is asking for the tenth root of 1024. The other inverse is if the exponent is unknown, for example: 2x = 1024 Solving this problem is called calculating the logarithm.
What is the difference between solving a problem and analyzing a problem?
When you analyze a problem you look it over which is what analyzing means. You look over the problem and then you solve it. When you solve a problem you solve it and you use certain steps and solve it but of course everyone has there ways to solve a problem but some people have ways to solve it by just analysing it. That is the difference.
