# What power do you raise 3 to to get 9

• m0286
In summary, Daniel is trying to figure out what power he needs to raise 16 to get 2. He uses his calculator to try different solutions, but all of them give him a number that is not 2. He eventually finds that 0.25 is the correct answer.
m0286
Hello again..
Alright I am now on the part of 12th grade calculus, dealing with logs and exponents and stuff. I understand if say log39 That its basically what power do you raise 3 to to get 9. Well a question i need to answer is log162. So what power to I raise 16 to to get 2? I used my calculator just trying to find a number that would work, and i got 0.25. How would I show work for that? all of the solutions they gave for different equations worked different like for the log39They showed 2 ways:
3^x=9
3^x=3^2
x=2
OR
log39=log3(3^2)
=2
None of these solutions work for 16 since 2 is 2^1 and 16^1 is 16 not 2... I am confused.. Is 0.25 even the right answer.
Any Help is appreciated greatly!
Thanks ya!

Last edited:
hint: 16=2^4

Yes.Use this property of the logarithms wrt a change of basis.

$$\log_{16}2=\frac{\ln 2}{\ln 16}=\frac{\ln 2}{4\ln 2}=\frac{1}{4}=0.25$$

Daniel.

Have you heard of a change of base? You calculator can only do log base 10. Here is the formula

$$\log_b a = \frac {\log_c a}{\log_c b}$$ where c can be anything. But why not set that to 10 so your calculator can crunch it.

0.25 is the correct answer, because 16^(0.25) = 2.

The easiest way to compute logs like $\log_b x$ on a calculator is to compute

$$\log_b x = \frac{\log x}{\log b}$$

where the logs on the right can be any base at all (10, e, whatever). In other words, to find $\log_{16} 2$ on your calculator, punch up (log 2 / log 16).

- Warren

Thanks, but what does the In stand for...

I don't think so.Any (scientifical) calculator should have natural logarithm.It's eseential.

Daniel.

m0286 said:
Thanks, but what does the In stand for...

That's probably "ln", the "natural logarithm", and it means the logarithm to the base e=2.1718..., if you haven't met it in your class yet, it's probably not far off.

Dexter's post using natural logs can just as well be done with logs of any base, including 10.

- Warren

## 1. What is the power that you raise 3 to in order to get 9?

The power that you raise 3 to in order to get 9 is 2. This can be expressed as 32 = 9.

## 2. How do you calculate the power of 3 that results in 9?

To calculate the power of 3 that results in 9, you can use the logarithm function. Specifically, the base 3 logarithm of 9 is equal to 2.

## 3. Can you explain the relationship between 3, the power, and 9 in this equation?

The relationship between 3, the power, and 9 in this equation is that 3 raised to the power of 2 (or 32) results in 9. In other words, 2 is the exponent or power that is used to raise 3 to get 9.

## 4. How can I generalize this concept to solve similar equations with different numbers?

To generalize this concept, you can use the formula ax = b, where a is the base, x is the power, and b is the result. In the case of our example, a = 3, x = 2, and b = 9. So, in general, to solve for x, you can use the formula x = logab.

## 5. What is the significance of this equation in mathematics?

This equation is significant in mathematics because it demonstrates the fundamental concept of exponentiation. It shows how a base number can be raised to a certain power to result in a specific number. This concept is used in many mathematical and scientific calculations and is essential in understanding more complex equations and functions.

• Calculus
Replies
3
Views
282
• Calculus
Replies
4
Views
1K
• Calculus
Replies
3
Views
2K
• Calculus
Replies
4
Views
291
• Calculus
Replies
2
Views
1K
• Calculus
Replies
1
Views
2K
• Calculus
Replies
14
Views
1K
• MATLAB, Maple, Mathematica, LaTeX
Replies
4
Views
540
• Calculus
Replies
4
Views
1K
• Calculus
Replies
5
Views
1K