SOLUTION: what is the exact log of log 6 base 2 mulitplied by log 8 base six? I'm confused b/c they both have different bases so I cant just add the eight and six
Algebra.Com
Question 674455: what is the exact log of log 6 base 2 mulitplied by log 8 base six? I'm confused b/c they both have different bases so I cant just add the eight and six
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You need to convert so that the two logs are the same base. You can convert the base 2 log to base 6, or the base 6 log to base 2, or convert both to some other base -- in the end it won't matter because you will always get the same answer.
Conversion formula:
 = \frac{\log_c(x)}{\log_c(b)})
Let's convert the base 6 log to base 2.
 = \frac{\log_2(8)}{\log_2(6)})
Now let's do the original multiplication:
\,\cdot\,\frac{\log_2(8)}{\log_2(6)})
Which simplifies to:
)
But wait! There's more! Now what would you pay? Oh, sorry, this isn't a Ginzu Knives infomercial, is it...but there is more for all that.
Note that 
, so:
)
But, remember:
\ =\ n\log_b(x))
So
)
But then:
\ =\ 1)
So
\,\cdot\,\log_6(8)\ =\ 3)
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
I hope someone can lend a hand on this one. I have tried several different ways to solve... (answered by orca)
How do i find the nth term for these sequences?
a) log [base 3], log [base 9] 81, log... (answered by Earlsdon)
Hey,
Quick question. I have the following problem:
Using properties of logarithms,... (answered by asuar010,solver91311)
What is...
2 log x - 1/2 log y
(they both have no base/the same base)
Only to be... (answered by nerdybill)
Using log rules
Loga = 0.3
Logb = -0.5
Solve
log(1000a^2)
log(4throot... (answered by Alan3354)
1/2 log base 8 (x+5) - 3 log base 8 y
this is what i have so far
=log base... (answered by stanbon)
What is the exact value of this expression?
Log base 9 of 1/3
I want to know if the... (answered by rothauserc)
Rewrite each expression as a single logarithm:
a) log 2 + log x – (log 3 + log y)
b)... (answered by Alan3354)
What is the value of x in log base x (log base 2(log base 2(log base x 9) = 0?
I need ur (answered by josmiceli)
