# Thread: Logarithm: Fractional exponents

1. ## 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

2. ## Re: Logarithm: Fractional exponents

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?

3. ## Re: Logarithm: Fractional exponents

ohh sorry, my mistake xD That was still 5 square root of 5. Thanks

4. ## Re: Logarithm: Fractional exponents

It's because $\displaystyle \sqrt{5} = 5^{\frac{1}{2}}$, so $\displaystyle 5\sqrt{5} = 5^1 \cdot 5^{\frac{1}{2}} = 5^{1 + \frac{1}{2}} = 5^{\frac{3}{2}}$.

5. ## Re: Logarithm: Fractional exponents

I forgot about that , tnx but how about no.1?

6. ## 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