Thread: Log Problem

Hi,

I am having some difficulty beginning to solve the following logarithm problem:
Any help is very much appreciated!

log3 (logx (log416) ) = -1 (Where 3, x, and 4 are all bases of the logs)

I was thinking of booting the log to get:

logx (log416) = 3^-1

Then going:

logx2 = 3^-1

Then I'm stuck.

Any suggestions?

Thanks,

Jim.

Originally Posted by jimstewart_NC

Hi,

I am having some difficulty beginning to solve the following logarithm problem:
Any help is very much appreciated!

log3 (logx (log416) ) = -1 (Where 3, x, and 4 are all bases of the logs)

I was thinking of booting the log to get:

logx (log416) = 3^-1

Then going:

logx2 = 3^-1

Then I'm stuck.

Any suggestions?

Thanks,

Jim.

Hi Jim,

$\displaystyle \log_x2=\frac{1}{3}$

$\displaystyle x^{1/3}=2$

$\displaystyle x^{1/3}=8^{1/3}$

$\displaystyle x=$

How's that?

Originally Posted by jimstewart_NC

Hi,

I am having some difficulty beginning to solve the following logarithm problem:
Any help is very much appreciated!

log3 (logx (log416) ) = -1 (Where 3, x, and 4 are all bases of the logs)

I was thinking of booting the log to get:

logx (log416) = 3^-1

Then going:

logx2 = 3^-1

Then I'm stuck.

Any suggestions?

Thanks,

Jim.

$\displaystyle 3^{-1} = \frac {1}{3}$

Therefore:

$\displaystyle x^{\frac {1}{3}} = 2$

Take the log (base 2) of both sides:

$\displaystyle \log_2 {x^\frac {1}{3}} = \log_2 2$

$\displaystyle \frac {1}{3} \cdot \log_2 x = 1$

$\displaystyle \log_2 x = 3$

$\displaystyle x = 2^3$

$\displaystyle x = 8$

Thank you topher0805 and masters, I really appreciated your help.

Oh, how do you get your superscript and subscript for exponents to show up?

Thanks,

Jim.

Originally Posted by jimstewart_NC

Thank you topher0805 and masters, I really appreciated your help.

Oh, how do you get your superscript and subscript for exponents to show up?

Thanks,

Jim.

To do superscript: 8^x = $\displaystyle 8^x$

Subscript: x_i = $\displaystyle x_i$

You just need to put [tex] tags around the stuff that is math. There is a shortcut key that looks like a sigma sign.