What is the solution to 6^log x = 1/36?

  • Thread starter Thread starter Coco12
  • Start date Start date
  • Tags Tags
    Logarithm
Click For Summary

Homework Help Overview

The problem involves the equation 6^log x = 1/36, which is situated within the context of logarithmic functions and exponentiation. Participants are exploring the implications of this equation and the relationship between the logarithm and its base.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss how to approach solving the equation, with some suggesting taking the logarithm of both sides. There is confusion regarding the interpretation of 1/36 as an exponent and its relation to the logarithm. Questions arise about the base of the logarithm being used.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants have offered guidance on taking logarithms and considering the base, while others express uncertainty about the correct approach and the implications of their calculations.

Contextual Notes

There is a noted lack of clarity regarding the base of the logarithm, which is not specified in the problem statement. This has led to differing assumptions among participants about how to proceed with the solution.

Coco12
Messages
272
Reaction score
0

Homework Statement



6^log x=1/36

2. Homework Equations
Y=logcx

The Attempt at a Solution


How do u solve this? I know the 1/36 is the exponent. Usually the logs that u normally do is not in an exponent like this. The answer is 0.01. How did they get that?
 
Physics news on Phys.org
Coco12 said:

Homework Statement



6^log x=1/36

2. Homework Equations
Y=logcx

The Attempt at a Solution


How do u solve this? I know the 1/36 is the exponent. Usually the logs that u normally do is not in an exponent like this. The answer is 0.01. How did they get that?


Take the log of both sides. Use rules of logs and solve for log(x). If you want to take a shortcut, 1/36=6^(-2), right?
 
I thought the ans was -2 since 6^-2 = 1/36

But the ans is 0.01. So that means it is not...
 
Coco12 said:
I thought the ans was -2 since 6^-2 = 1/36

But the ans is 0.01. So that means it is not...

log(x)=(-2). x isn't -2. You are supposed to solve for x. What's the base of your logarithms?
 
Is the base 10?
 
Coco12 said:
Is the base 10?

It should be stated in the problems or your book what the base is. Suppose it is 10. Then if log(x)=(-2), what is x?
 

Similar threads

Replies
10
Views
2K
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
7
Views
2K
  • · Replies 11 ·
Replies
11
Views
6K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 10 ·
Replies
10
Views
2K