Log help please

**AZIZMARS** · April 11th 2010, 04:28 PM

Hey guys can anyone explain to me how to do this problem
Logx243=5/3
base is x
Thanks for the help guys

**stapel** · April 11th 2010, 04:34 PM

Originally Posted by AZIZMARS

Logx243=5/3
base is x

Use the relationship between logs and exponentials:

. . . . . $y\, =\, x^b$

. . . . .means the same thing as

. . . . . $\log_b(y)\, =\, x$

...to convert the log equation into the corresponding exponential equation. Then convert "243" to a power of three.

**AZIZMARS** · April 11th 2010, 04:35 PM

Yeah I kind of understood that but idk why im getting stuck after that part can you please continue on that? thank you

**stapel** · April 11th 2010, 04:43 PM

In future, please include what you've been able to do, so we don't waste your time repeating what you've aready got.

Please reply showing what you've done, up through the restating of 243. Thank you!

**AZIZMARS** · April 11th 2010, 04:45 PM

Im sorry i apologize well as of right now i understand this

Logx243=5/3
means
243=x^5/3
and then you make the 243 into
3^5=x^5/3
but then after that i dont understand what to do
and once again I apologize for not saying what i had understood up to.

**stapel** · April 11th 2010, 04:48 PM

Originally Posted by AZIZMARS

Logx243=5/3
means
243=x^5/3
and then you make the 243 into
3^5=x^5/3
but then after that i dont understand what to do

Find a way to convert the right-hand side into something equivalent to the left-hand side.

. . . . . $x^{\frac{5}{3}}\, =\, \left(x^3\right)^5$

What then does $x^3$ equal? Then what is $x?$

**AZIZMARS** · April 11th 2010, 04:52 PM

Originally Posted by stapel

Find a way to convert the right-hand side into something equivalent to the left-hand side.

. . . . . $x^{\frac{5}{3}}\, =\, \left(x^3\right)^5$

What then does $x^3$ equal? Then what is $x?$

Im pretty sure the awnser would be 3 = x^(1/3) but im still not very sure on how i got that awnser.

**AZIZMARS** · April 11th 2010, 05:58 PM

Anyone able to help me please? I just need to know how to awnser this question step by step with an explaination please

**HallsofIvy** · April 12th 2010, 03:19 AM

$3^5= x^{5/3}= (x^{1/3})^5$ .

Taking the fifth root of each side, $3= x^{1/3}$ .

Now cube each side.

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