How would i work this out? (125/8)^n = 25/4 NON CALCULATOR PLEASE. thanks x ?

Question

How would i work this out? (125/8)^n = 25/4 NON CALCULATOR PLEASE. thanks x ?

Answer 1

take the ln

n ln(125/8) = ln(25/4)

n ln[(5/2)^3] = ln[(5/2)^2]

3n ln[5/2] = 2ln[5/2]

3n = 2

n = 2/3

check.

(125/8)^(2/3)

cube root of 125 = 5 and 5^2 = 25

cube root of 8 = 2 and 2^2 = 4

(125/8)^(2/3) = 25/4 which is the original equation

Answer 2

The first thing I notice is that 125 and 25 have the same base as does 8 and 4

125 = 5^3 and 25 = 5^2

8 = 2^3 and 4 = 2^2

(5^3/2^3)^n = (5^2/2^2)

distribute the n

(5^3n)/(2^3n) = (5^2/2^2)

set the bases equal to each other

5^3n= 5^2

2^3n = 2^2

so 3n = 2

n = 2/3