HELP! Please help with this math problem!?

Question

log 4 of (2 times the fifth root of 8) minus log 8 of the 3rd root of 0.25


Sorry i couldnt type it out with numbers.

please give the steps

THANK YOU!

Answer 1

Interpreting your question is a bit confusing, but I'm going to assume that it is this:

log[base 4] ( 2 * 8^(1/5) ) - log [base 8] ( (0.25)^(1/3) )

Separating the first log into two logs,

log[base 4] (2) + log[base 4](8^(1/5)) - log[base 8] ( (0.25)^(1/3) )

We can move the exponents within the logs outside of the logs. We can also convert 0.25 into a fraction, 1/4.

log[base 4](2) + (1/5) log[base 4](8) - (1/3) log[base 8] (1/4)

We can calculate log[base 4](2) directly; the answer is equal to 1/2, since 4 to the 1/2 is equal to 2.

(1/2) + (1/5) log[base 4](8) - (1/3) log[base 8] (1/4)

Converting log[base 4](8) using the change of base formula, we're going to choose base 2.

(1/2) + (1/5) [ (log[base 2](8)) / (log[base 2](4)) ]
- (1/3) [ (log[base 2](8)) / (log[base 2](1/4) ]

We can convert 1/4 into 4^(-1), and subsequently pull that (-1) power outside. This gives us

(1/2) + (1/5) [ 3/2 ] - (1/3) [ 3 / (-2) ]

(1/2) + (3/10) + (1/3)(3/2)

(1/2) + (3/10) + (1/2)

1 + 3/10

13/10

Answer 2

Express your logs and expressions all as powers of 2:

2*5thrt(8)=2*8^(1/5)
=2*2^(3/5)
=2^(8/5)

3drt(.25)=3drt(2^-2)=2^(-2/3)

Now the logs. log(4)x = log(2²)x = ½log(2)x, so
log(4)2^(8/5) = ½log(2)2^(8/5)
=½*8/5=4/5
Similarly, log(8)x = log(2³)x = (1/3)log(2)x, so
log(8)2^(-2/3) = (1/3)log(2)2^(-2/3)
=(1/3)*-2/3=-2/9

Finally, your subtraction:
4/5-(-2/9) = 4/5+2/9=46/45

Answer 3

4x2=8 8-5=3 3divide25=7.12

Answer 4

i dont know