Solve Logarithmic Equation: [log_{2} 9/log_{2} 10] - log 3

[nvez]

Homework Statement

I have to take the following equation and make it one single log

$$[log_{2} 9/log_{2} 10] - log 3$$

The answer is equal to: $$log 3$$

I usually know how to do this however I have no clue in this case, I have the answer however.

Homework Equations

None?
log x - log y = log (x/y)
log x + log y = log (x*y)

The Attempt at a Solution

I have tried the putting what the divison part really is equal too then subtracting it or whatever but to no avail.

I appreciate help in advanced.

 

[rock.freak667]

Try changing the base to log₁₀ (I assumed that is what log was)

 

[nvez]

Thank you very much!

For future reference:

log_c m = log_s m / log_s c

In this case:

log₂ 9 / log₂ 10 = log₁₀ 9

log 9 - log 3 = log (9/3) = log 3

Thanks again.

 

[Mark44]

Homework Statement

I have to take the following equation and make it one single log

$$[log_{2} 9/log_{2} 10] - log 3$$

A small point: this is not an equation. It's important to understand when you're working with an equation and when you're working with an expression, since the kinds of operations you can do are different. For example, if you're working with an equation, you can add a quantity to both sides, multiply both sides by a quantity, and so on, but you're very limited in the things you can do with just an expression.

 

[nvez]

A small point: this is not an equation. It's important to understand when you're working with an equation and when you're working with an expression, since the kinds of operations you can do are different. For example, if you're working with an equation, you can add a quantity to both sides, multiply both sides by a quantity, and so on, but you're very limited in the things you can do with just an expression.

Ahh, I see!

Thank you very much again! :)