Solve each equation

Question

a) (1/5)^x = 125

b) 36^x-1 = 216

c) 4^(x)*2^(-x+4)=(1)/(8)

Answer 1

a)

(1/5)^X = 5^3 Now get log from both sides:

X log (1/5) = 3 log 5

X(log1 - log5) = 3 log 5, we know log 1 = 0 so:

-X log 5 = 3 log 5 Cancel log 5 from both sides, so: X = -3

b)

6^(2(X-1)) = 6^3 Get log from both sides:

2(X-1) log 6 = 3 log 6 Now cancel log 6 (or divide both sides by log 6)

2X - 2 = 3

2X = 5

X = 2.5

c)

2^2X * 2^(-X + 4) = 1/2^3

2X log2 + (-X + 4) log 2 = log 1 - 3log2 we know log 1 = 0 so

log2 (2X -X + 4) = -3 log 2 Divide both sides by log 2 then solve the equation.

X + 4 = -3 So X = -7.