# Logarithm: Fractional exponents

• March 19th 2013, 11:43 PM
KerkLu
Logarithm: Fractional exponents
1. x2/3=4 //Really dont know T_T

2. 5x=square root of 5
~ 5x= 5 * 51/2
~ 5x = 53/2 //How did 3/2 happen? - .-

I dont know how to solve the ff fractional fractional exponents. please explain to me step by step. T_T
• March 20th 2013, 12:01 AM
Prove It
Re: Logarithm: Fractional exponents
Quote:

Originally Posted by KerkLu
1. x2/3=4 //Really dont know T_T

2. 5x=square root of 5
~ 5x= 5 * 51/2
~ 5x = 53/2 //How did 3/2 happen? - .-

I dont know how to solve the ff fractional fractional exponents. please explain to me step by step. T_T

First of all, in question 2, you can not turn $\displaystyle \sqrt{5}$ into $\displaystyle 5\sqrt{5}$. Are you sure you wrote down the question properly?
• March 20th 2013, 12:06 AM
KerkLu
Re: Logarithm: Fractional exponents
ohh sorry, my mistake xD That was still 5 square root of 5. Thanks :)
• March 20th 2013, 12:13 AM
Prove It
Re: Logarithm: Fractional exponents
It's because $\displaystyle \sqrt{5} = 5^{\frac{1}{2}}$, so $\displaystyle 5\sqrt{5} = 5^1 \cdot 5^{\frac{1}{2}} = 5^{1 + \frac{1}{2}} = 5^{\frac{3}{2}}$.
• March 20th 2013, 12:28 AM
KerkLu
Re: Logarithm: Fractional exponents
I forgot about that , tnx :) but how about no.1?
• March 20th 2013, 04:50 AM
ibdutt
Re: Logarithm: Fractional exponents
x^2/3 = 4
Both the sides should be raised to the power os 3/2
Thus we have [x^2/3]^3/2 = 4^3/2 that gives x = [4^1/2]^3=2^3= 8