Can you please help with roots and powers?

Question

3) Find the value of x when

√125= 5^x

2) a=2^x, b=2^y

a) Express in terns of 'a' and 'b'

i) 2^x+y ii) 2^2x iii) 2^x+2y

ab = 16 and 2ab^2=16

b) Find the value of x and the value of y.

Thankyou.

Answer 1

3)

(125)^(1/2) = 5^x

(5^3)^(1/2) = 5^x

5^(3/2) = 5^x

Therefore x = 3/2

2)

a)

i)

2^x + y = a + log2(y)   (That means log base 2 of y)

ii)

2^(2x) = a^2

iii) 2^(x + 2y) = (2^x)*2^(2y) = a(b^2)

ab=16   and 2ab^2 = 16

(2^x)(2^y) = 16   and ab^2 = 8

2^(x+y) = 2^4   and    (2^x)*(2^(2y)) = 8

x + y = 4     and          2^(x + 2y) = 2^3

x + y = 4       and       x + 2y = 3

y = -1 and x = 5

Hope that helps.

Take care,

David

Answer 2

3) 125=5^3     root of 125= 5^(3/2)       x=3/2

2) Next time try to put the brackets (I had to put them. Did I get OK?)

a)   i)2^(x+y)= ab

      ii) 2^(2x)=a^2

      iii) 2^(x + 2y)=  a + b^2

b) 2 a b^2=16

    2 (a b)*b=16

    2b=1b=1/2

    a=16/b=32

Answer: a=32;b=1/2

3*)   128=2^7   sqrt128= 2^(7/2)

       2^(7/2)= 2^y

       y=7/2

Answer 3

Too much work for 1 question....one problem per question please

I'll show you #1

square both sides

125=5^2x

now 125=5^3

5^3=5^2x

compare exponents...they must be equal

3=2x

x=3/2  ANSWER