I forgot how to solve for an exponent

  • Thread starter bocobuff
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In summary, to solve for b in the equation f(x)=a*xb with the given information of f(1.5)=10 and f(1.7)=14, you need to plug in the values and set the resulting equations equal to each other. This will give you 2 equations and 2 unknowns, allowing you to solve for b using algebraic manipulation.
  • #1
bocobuff
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Homework Statement


i need to solve for b in f(x)=a*xb
i know f(1.5)=10 and f(1.7)=14

it's been forever since i did calc like this and i am blank on what to do.
i can't remember if or how i can set them equal to each other to solve for b.
i know i have 2 eqns and 2 unknowns.

do i set f(1.5)=f(1.7)? i don't think that's right but i can't think of what else to do??
 
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  • #2
bocobuff said:

Homework Statement


i need to solve for b in f(x)=a*xb
i know f(1.5)=10 and f(1.7)=14

it's been forever since i did calc like this and i am blank on what to do.
i can't remember if or how i can set them equal to each other to solve for b.
i know i have 2 eqns and 2 unknowns.

do i set f(1.5)=f(1.7)? i don't think that's right but i can't think of what else to do??

Why would you set them equal to each other? You know they equal 10 and 14 respectively so are you saying 10 = 14?

What you should do is plug it in, i.e. f(1.5) = a*1.5^b = 10 then do the same with the other point, now you will have 2 equations and 2 unknowns, so for example a = 10/1.5^b, figure out what a = in the other equation and set THOSE equal to each other.
 
  • #3
alright I'm an idiot.
so you get something like 14/10=(1.7/1.5)^b and then take natural log of each side right...?
 
  • #4
Assuming your algebra is correct, yes.
 
  • #5
sweet thanks a lot
 

What is an exponent?

An exponent is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is usually written as a superscript to the right of the base number.

How do I solve for an exponent?

To solve for an exponent, you can use the power rule which states that when multiplying exponential expressions with the same base, you add the exponents. For example, 23 * 24 = 27.

What is the difference between an exponent and a logarithm?

An exponent is the power to which a number is raised, while a logarithm is the inverse operation of exponentiation. In other words, a logarithm tells you what exponent you need to raise a certain base to get a given number.

What happens when I have a negative exponent?

A negative exponent indicates the reciprocal of the positive exponent. For example, 2-3 is the same as 1/(23) = 1/8.

What is the order of operations when solving for an exponent?

The order of operations for solving an expression with an exponent is the same as for any other mathematical expression, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

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