Rewriting y = 5x as 3kx: A Step-by-Step Guide

  • Thread starter the_awesome
  • Start date
In summary, the conversation involves rewriting the equation y = 5x in the form 3kx. The suggested method is to use logarithms, specifically the logarithm rule log a^b = b log a, to find the value of k. The conversation also includes a discussion about how to correctly use the method and some examples are provided.
  • #1
the_awesome
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Homework Statement


Rewrite y = 5x in the form 3kx


Homework Equations



no idea

The Attempt at a Solution



I can't really attempt this because i don't have a clue where to start. I've looked in all my maths books and it says nothing on how to do this. Our unit is partially based on inverses and differentation so I am guessing its something to do with that.

By guessing and typing random numbers into the calculator, i know that k is equal to 1.465

example :

52 = 25
31.465 x 2 = 25

thats all i can gather, but how do i show my working out/correct method? :(
 
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  • #2
well if you want 3^(kx)=5^x

take logs to find k.
 
  • #3
how do i do that?
 
  • #4
Have you studied logarithms?
If you have, use log a^b = b log a to find the value of k.
 
  • #5
do you know about logarithmic functions?

take the log of both sides and from the log laws, you can show log(y^k) = k.log(y)
 
  • #6
shramana said:
Have you studied logarithms?
If you have, use log a^b = b log a to find the value of k.
so u mean like...

(let a = 5)
(let b = 2)

log 52 = 2 log 5
= 1.39

but, the value of k should be 1.465.


what about...
5x = 3kx
0 = 5x - 3kx
0 = 5 -3k
3k = 5
k = (log 5) divided by (log 3)

therefore, k = 1.464973521

so...5x = 31.465x
 
Last edited:
  • #7
the_awesome said:
so u mean like...

(let a = 5)
(let b = 2)

log 52 = 2 log 5
= 1.39

but, the value of k should be 1.465.


what about...
5x = 3kx
0 = 5x - 3kx
0 = 5 -3k
No, that does not follow. You cannot just "cancel" exponents like that.
You can, directly from your original equation say that
5x= 3kx= (3k)x and NOW take the "xth" root of both sides: 5= 3k.

3k = 5
k = (log 5) divided by (log 3)

therefore, k = 1.464973521

so...5x = 31.465x
That works, with my correction to your reasoning. What people were suggesting you do is simpler: just take the logarithm of both sides of the original equation:
log(5x)= log(3kx)
x log(5)= kx log(3)
Since this is to be true for all x, you can take x non-zero and divide both sides by x:
log(5)= k log(3) so k= log(5)/log(3).
 
Last edited by a moderator:
  • #8
ah i see, thanks for the help!
 

1. What is the purpose of rewriting y = 5x as 3kx?

The purpose of rewriting y = 5x as 3kx is to simplify the equation and make it easier to solve. By factoring out a common factor of 5, the equation becomes 3kx, where k represents the remaining terms of the original equation.

2. How do I know when to use this step-by-step guide?

This guide can be used whenever you encounter an equation in the form of y = ax, where a is a constant. By following the steps outlined in the guide, you can rewrite the equation as 3kx, making it easier to solve and manipulate.

3. Will rewriting the equation change the solution?

No, rewriting the equation will not change the solution. The two equations, y = 5x and 3kx, are equivalent and have the same solution. The only difference is that the latter is in a simplified form.

4. Can I use this technique for other equations?

Yes, this technique can be applied to other equations that have a common factor in the form of y = ax. By factoring out the common factor, you can rewrite the equation in a simplified form.

5. Why is it important to simplify equations?

Simplifying equations is important because it makes them easier to understand and work with. It also allows you to identify patterns and relationships between variables, making it easier to solve and manipulate the equation to find the desired solution.

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