SOLUTION: I need help with a few problems. I am stuck. 1) Write the equation (1/5)^-7 = 78125 in logarithmic form. 2) Simplify the expression (256x^4y)^1/4/(81xy^3)^3/4 Assume that a

Question 192974: I need help with a few problems. I am stuck.
1) Write the equation (1/5)^-7 = 78125 in logarithmic form.
2) Simplify the expression (256x^4y)^1/4/(81xy^3)^3/4 Assume that all variables represent positive numbers
3) Find the value of x: log 3 27 = x
4) Assume that all variables are positive and multiply y^2/6(y^-2/6 + 8y^4/6)
Any and all help will be appreciated.
Thanks in advance!!
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
1)(1/5)^-7=78125
(5/1)^7=78125
5^7=78125 ok
log to base 5 of 78125=7
checklog78126/log5=7 ok
2) ( (256x^4y)^(1/4))/( (81xy^3)^(3/4))
num
256^.25=4
(x^4)^.25=x^1=x
den
81^(3/4)= (81^.25)^3=3^3=27
(y^3)^(3/4)=(y^(9/4)
combining
( 4*x*y^.25)/ ( 27*x^.75*y^(9/4))
remember to divide common bases,, subst exponents
(4x^.250/(27y^2)
check, let x=2, y=3
answer (4*2^.25)/(27*3^2) =.01957
original ((256*2^4*3)^.25)/( ( 81*2*3^3)^.75)
10.5286/537.85 = .0196 ok

3) log base 3 of 27 = x
log27/log3=3=x
check 3^3=27 ok
4) (y^(2/6))*(y^(-2/6)+8y^(4/6))
y^(2/6-2/6) +8 y^(2/6+4/6)
Y^0 +8y^1
1+8y
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