Exercise 6 Page 301

To solve the given exponential equation, we will start by rewriting the terms so that they have a common base. Note that

8

cannot be represented as a natural power of

4 .

Therefore, we will write both

4

and

8

as the powers of

2 .

4^{3 x} = 8^{x + 1}

Write as a power

(2^{2})^{3 x} = (2^{3})^{x + 1}

$(a^{m})^{n} = a^{m \cdot n}$

2^{2 \cdot 3 x} = 2^{3 (x + 1)}

2^{6 x} = 2^{3 (x + 1)}

Distribute $3$

2^{6 x} = 2^{3 x + 3}

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal.