6^x=4

**weasley74** · February 11th 2008, 12:10 PM

6^x=4 ? i have a sudden black out and i can't remember the rule for when solving equations like this one.. to complicate things i'm not allowed to answer with x=log4/log6

**yellow4321** · February 11th 2008, 01:03 PM

when two logs are divided they can be written thus:

x= log(4/6)

same as

x= log4 - log6

**weasley74** · February 11th 2008, 01:05 PM

and what about if log isn't allowed to be in the answer at all?

**topher0805** · February 11th 2008, 01:08 PM

Are you familiar with the change of base formula?

**weasley74** · February 11th 2008, 01:10 PM

I don't think so.. it's possible that I am, just that it has a very different name in Swedish.. ^^

**yellow4321** · February 11th 2008, 01:11 PM

enter it into a calculator you could also write it as x=log (base 4) *6

could you tell me the question in full?

**topher0805** · February 11th 2008, 01:13 PM

Are you not allowed to use a calculator? If you are then you can find the exact value.

**weasley74** · February 11th 2008, 01:14 PM

here's the kicker.. i'm not allowed to use a calculator ^^ yay (not so much)

^6 log4..

**angel.white** · February 11th 2008, 01:19 PM

Originally Posted by weasley74

6^x=4 ? i have a sudden black out and i can't remember the rule for when solving equations like this one.. to complicate things i'm not allowed to answer with x=log4/log6

Method1:
Initial equation
$6^x=4$

Take the log of both sides (it doesn't matter what base you use)
$log(6^x)=log(4)$

One of the properties of logs is that if they are the log of a number to a power, they are the same as the power times the log of the number. Meaning $log(6^x)=xlog(6)$ so
$xlog(6)=log(4)$

Divide both sides by log(6)
$x=\frac {log(4)}{log(6)}$

Method2
Initial equation
$6^x=4$

Take log base 6 of both sides
$log_6(6^x) = log_6(4)$

Simlify
$x = log_6(4)$

Use change of base formula to rewrite in a format you can plug into a calculator. Change of base formula says $log_a(b) = \frac{log_c(b)}{log_c(a)}$ This works for any value of c. Typically the value chosen is 10 or e, as log base ten and log base e (natural log) are the two most common logs, and are programmed into any decent calculator.
$x = \frac{log(4)}{log(6)}$

**angel.white** · February 11th 2008, 01:21 PM

Originally Posted by topher0805

Are you not allowed to use a calculator? If you are then you can find the exact value.

$x=\frac{log(4)}{log(6)}$
is the exact value. A decimal value is not exact, it is an approximation, because it cannot get to every digit in the decimal place (if the value is irrational).

**OzzMan** · February 11th 2008, 01:28 PM

I thought the poster said you can't answer with log

**weasley74** · February 11th 2008, 01:31 PM

Originally Posted by OzzMan

I thought the poster said you can't answer with log

correct.

**angel.white** · February 11th 2008, 01:32 PM

Originally Posted by OzzMan

I thought the poster said you can't answer with log

Then the answer he is looking for is
$x = \frac{log(4)}{log(6)} \approx$ 0.77370561446908317374049227693595

Which is not exact, and I would seem to require a calculator to find.

It seems most likely to me that they are looking for $x=\frac{log(4)}{log(6)}$ or $x=log_6(4)$ as these values are exact, and one of the other requirements was that he could not use a calculator.

**OzzMan** · February 11th 2008, 01:34 PM

What math class is this for? The only way i know how to answer this problem is with logarithms lol. This is interesting.

**OzzMan** · February 11th 2008, 01:35 PM

There must be another way to do this without logarithms.

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