**Algebra
Rules for Exponential Functions:**

If , then a^{n} is the product
of n a’s.

For example,

Examples of exponential equations with the same bases

**Example No.1:**

Solve

**Solution:**

(Equate the exponents)

(Subtract 1 from both sides)

(simplify it)

**Example No.2:**

Solve

**Solution:**

(Equate the exponents)

(Add 4 from both sides)

(simplify it)

(Divide on both sides by 2)

(finally simplify it)

Examples of exponential equations with the unlike bases

**Example No.1:**

Solve

**Solution:**

(Rewrite 64 as 4^{3})

(Equate the exponent to obtain the value of x)

**Example No.2:**

Solve

**Solution:**

(Rewrite 9 as 3^{2})

(Power of a power property)

(Equate the exponents)

(Subtract both side by 2)

(Simplify it)

Examples of solving exponential equation when 0 < b < 1

**Example No.1:**

Solve

**Solution:**

(Rewrite 1/2 as 2^{-1} and 9 as 3^{2})

(Power of a power property)

(Equate the exponents)

(Solve for x)

**Example No.2:**

Solve

**Solution:**

(Rewrite 16 as 2^{4})

(Definition of negative exponent)

(Equate the exponents)

(Subtract both sides by 1)

(solve for x)