# Math Help - Need help with logarithm problem

1. ## Need help with logarithm problem

My step daughter presented me with this problem. I am usually pretty good at math but this one had me stumped. I couldn't understand how they got from the first step to the second. From the second step I could easily solve it. Please explain how they got to this so I can explain it to her. Thanks a ton in advance.

Original Problem:

Step 2:

2. Originally Posted by gfox5
My step daughter presented me with this problem. I am usually pretty good at math but this one had me stumped. I couldn't understand how they got from the first step to the second. From the second step I could easily solve it. Please explain how they got to this so I can explain it to her. Thanks a ton in advance.

Original Problem:

Step 2:

sorry, but $\sqrt{8} \ne 4^{\frac{3}{2}}$

$\sqrt{8} = 2^{\frac{3}{2}}$

did you leave something out?

3. no, that is exactly what they had. And that is what we thought. We couldn't figure out how they got that. We thought it might be a mistake in the program. it is a disc that her teacher gave out for them to do the problems on the software as homework. We couldn't figure out how they got to that. It didn't make sense to us. We came to the conclusion that she would just have to ask her teacher tomorrow at school.

4. Originally Posted by gfox5
My step daughter presented me with this problem. I am usually pretty good at math but this one had me stumped. I couldn't understand how they got from the first step to the second. From the second step I could easily solve it. Please explain how they got to this so I can explain it to her. Thanks a ton in advance.

Original Problem:

Step 2:

Picking up from what skeeter was saying.

$\sqrt{8} = 2^{\frac{3}{2}} = 2^{\frac{2\times 3}{4}}= (2^2)^{\frac{ 3}{4}} = 4^{\frac{ 3}{4}}$

Therefore $\log_4\sqrt{8} = \log_44^{\frac{ 3}{4}}= \frac{ 3}{4} \log_44 = \frac{ 3}{4}$