# Solve for x, 64^{x}= 16^{(x-1)}

**Solution:**

Let us solve the given equation 64^{x}= 16^{(x-1)} using the exponent rule.

**Step 1:**

**Make equivalent expressions using the equal base.**

⇒ 64^{x}= 16^{(x -1)} can be written using equal base as:

(4)^{3x} = (4) ^{2(x -1)}

Since the base of both the equations are equal.

**Step 2:**

**Use the exponent rule x ^{a} = x^{b},**

then a = b,

Where x = 4, a = 3x and b = 2(x -1)

3x = 2(x - 1)

3x = 2x - 2

**Step 3:**

**Subtract 2x from both sides.**

3x - 2x = - 2

X = - 2

**Thus, the value of x which satisfies the equation 64 ^{x}= 16^{(x-1)} is - 2.**

**Summary:**

## Solve for x, 64^{x}= 16^{(x-1)}

The value of x is - 2 for the equation 64^{x}= 16^{(x-1)}.

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