How do you evaluate this log equation?

[haengbon]

Homework Statement

log₃9 + log₄1/64 + log₅1

Homework Equations

none

The Attempt at a Solution

I tried answering it by...

(3^x=9) + (4^x=1/64) + (5^x=1)
because of this, I got 5. Is that correct?

 

[tiny-tim]

Hi haengbon!

(3^x=9) + (4^x=1/64) + (5^x=1)
because of this, I got 5. Is that correct?

Correct method , but wrong result …

try (4^x=1/64) again. ​

 

[haengbon]

Hi haengbon!


Correct method , but wrong result …

try (4^x=1/64) again. ​

I tried it again and got -3 for 4^x=1/64 :D is that correct now? ^^ thank you for the help by the way :)

 

[tiny-tim]

I tried it again and got -3 for 4^x=1/64 :D is that correct now? ^^

Yup!

 

[Mark44]

I tried answering it by...

(3^x=9) + (4^x=1/64) + (5^x=1)
because of this, I got 5. Is that correct?

If you turn in work like this, your instructor will probably deduct points, since you are apparently trying to add three equations.

Each of the log expressions is simple enough to calculate, so your work should look something like this.

log₃9 + log₄1/64 + log₅1
= 2 - log₄64 + 0
= 2 - 3 = -1

I used the fact that log(1/x) = - log(x) going from the first expression to the second.