Converting a log equation to exponential equation

In summary, the conversation discusses graphing the equation f(x) = log5 (x) + 3, with the base of 5. The questioner is curious about the exponential form and if it should be in the general math section. The responder provides the exponential form and how to solve for x.
  • #1
wScott
88
0

Homework Statement


the question asks to graph the equation:
(don't know how to use latex sorry)
f(x) = log5 (x) + 3 where the 5 is the base
Just for my curiosity what would the exponential equation be?
I can graph it, just can't get the exponential form
Tell me if this should go in the general math section.
 
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  • #2
You already put it in the general math section lol, look there for the working.
[tex]5^{f(x)} = 125x[/tex]
 
  • #3
Can that be expressed as x=? and can you show me how you did that?
 
  • #5
wScott said:

Homework Statement


the question asks to graph the equation:
(don't know how to use latex sorry)
f(x) = log5 (x) + 3 where the 5 is the base
Just for my curiosity what would the exponential equation be?
I can graph it, just can't get the exponential form
Tell me if this should go in the general math section.

"Solve" for x: y- 3= log5(x) so, using the definition of log5(x) as the inverse of 5x, x= 5y-3= (1/125)5y.
 

1. How do you convert a log equation to an exponential equation?

To convert a log equation to an exponential equation, you can use the following formula: logb(x) = y is equivalent to by = x. This means that the base of the logarithm becomes the base of the exponential, the argument of the logarithm becomes the power of the exponential, and the result of the logarithm becomes the value of the exponential equation.

2. What is the purpose of converting a log equation to an exponential equation?

Converting a log equation to an exponential equation can help simplify the problem and make it easier to solve. It also allows you to work with the equation in a different form, which may be more useful for certain calculations or applications.

3. Can you provide an example of converting a log equation to an exponential equation?

Sure. Let's say we have the log equation log2(8) = 3. To convert this to an exponential equation, we use the formula by = x, so we get 23 = 8. Therefore, the exponential equation equivalent of log2(8) = 3 is 23 = 8.

4. Are there any rules or restrictions when converting a log equation to an exponential equation?

Yes, there are a few rules to keep in mind when converting a log equation to an exponential equation. The base of the logarithm must be positive and not equal to 1, the argument of the logarithm must be positive, and the result of the logarithm must be a real number. If these conditions are not met, the conversion may not be possible.

5. Can you convert any log equation to an exponential equation?

No, not all log equations can be converted to exponential equations. As mentioned before, there are certain rules and restrictions that must be met in order for the conversion to be possible. Additionally, some log equations may not have an equivalent exponential form, so the conversion is not possible.

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