Question

Solve the following equations:

(a) 8^x = 64
(b) 9^x = 27
(c) 4^x = 128
(d) 2^x * 2^(x+1) = 1/2

Answer 1

To solve the given equations, we can use the rule of exponents and algebraic manipulation to find the values of x.

Step-by-step explanation:

To solve the given equations:

(a) 8^x = 64

Since 8^2 = 64, x = 2

(b) 9^x = 27

Since 9^2 = 81, x = √27 = 3/2

(c) 4^x = 128

Since 4^3 = 64, x = 3

(d) 2^x * 2^(x+1) = 1/2

Using the rule of exponents, 2^(2x+1) = 1/2

Rewriting 1/2 as 2^(-1), we have 2^(2x+1) = 2^(-1)

Equating the exponents, 2x + 1 = -1

Solving for x, we get x = -1