How to write this logarithmic equation as a power

In summary, the relationship between y and x in the form Iny = 3+0.2x can be written as y = pq^x, where p = exp(3) and q = exp(0.2). This is because ln(a)=x means a=exp(x) and exp(x+y)=exp(x)*exp(y), which can be applied to the original equation to get y = exp(3+0.2x). Then, using the property a^(b*c)=(a^b)^c, we can rewrite this as y = exp(3+0.2x) = exp(3) * exp (0.2x). Therefore, the final form is y = pq^x
  • #1
brandon26
107
0
how can the relationship between y and x in the form Iny = 3+0.2x, be written in the form y = pq^x.

I tried many ways, but can't find the righ format, someone help please?
 
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  • #2
1) ln(a)=x means a=exp(x)
2) exp(x+y)=exp(x)*exp(y)
 
  • #3
yes, but that doesn't help me? :confused:
 
  • #4
1)lny=3+0.2x => y=exp(3+0.2x). Now you do the 2).
 
  • #5
Oh right. Thank you. I got y=exp(3) * exp (0.2x).
That becomes y = exp(3+0.6) * exp(x)
 
  • #6
Sorry that is wrong
 
  • #7
y = exp(0.2)x + exp(3). is that right?
 
  • #8
sorry, i forgot this one:)
3)a^(b*c)=(a^b)^c
 
Last edited:

1. How do I convert a logarithmic equation into a power equation?

To convert a logarithmic equation into a power equation, you can use the property of logarithms that states logb(xy) = ylogb(x). This means that you can rewrite a logarithmic equation as an exponent, where the base of the logarithm becomes the base of the exponent and the argument of the logarithm becomes the power.

2. Can any logarithmic equation be written as a power equation?

Yes, any logarithmic equation can be written as a power equation using the property mentioned above. However, not all power equations can be written as logarithmic equations, so it is important to check if the conversion is possible before proceeding.

3. What is the difference between a logarithmic equation and a power equation?

A logarithmic equation is an equation that contains a logarithm, which is the inverse function of a power. In other words, a logarithmic equation is written in the form logb(x) = y, where x is the power to which the base b is raised. On the other hand, a power equation is an equation where the variable appears as an exponent.

4. Are there any special rules for converting logarithmic equations with different bases into power equations?

Yes, there is a special rule known as the change of base formula, which states that logb(x) = loga(x) / loga(b). This formula allows you to change the base of the logarithm, making it easier to convert a logarithmic equation with a different base into a power equation.

5. How can converting a logarithmic equation into a power equation be useful?

Converting a logarithmic equation into a power equation can be useful in simplifying complex equations, solving exponential and logarithmic equations, and graphing functions. It can also help in solving real-world problems that involve exponential growth or decay.

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