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

2. Originally Posted by AZIZMARS
Logx243=5/3
base is x
Use the relationship between logs and exponentials:

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

. . . . .means the same thing as

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

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

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

4. 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!

5. 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.

6. 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.

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

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

7. Originally Posted by stapel
Find a way to convert the right-hand side into something equivalent to the left-hand side.

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

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

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

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

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

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

Now cube each side.