Solve for x 2*4^(x-3)=16

$2 \cdot 4^{x - 3} = 16$

Step 1

Rewrite $4$ as $2^{2}$ .

$2 \cdot {(2^{2})}^{x - 3} = 16$

Step 2

Multiply the exponents in ${(2^{2})}^{x - 3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \cdot 2^{2 (x - 3)} = 16$

Apply the distributive property.

$2 \cdot 2^{2 x + 2 \cdot - 3} = 16$

Multiply $2$ by $- 3$ .

$2 \cdot 2^{2 x - 6} = 16$

Step 3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{1 + 2 x - 6} = 16$

Step 4

Subtract $6$ from $1$ .

$2^{2 x - 5} = 16$

Step 5

Create equivalent expressions in the equation that all have equal bases.

$2^{2 x - 5} = 2^{4}$

Step 6

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 x - 5 = 4$

Step 7

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $5$ to both sides of the equation.

$2 x = 4 + 5$

Add $4$ and $5$ .

$2 x = 9$

Divide each term in $2 x = 9$ by $2$ and simplify.

Divide each term in $2 x = 9$ by $2$ .

$\frac{2 x}{2} = \frac{9}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{9}{2}$

Divide $x$ by $1$ .

$x = \frac{9}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{2}$

Decimal Form:

$x = 4.5$

Mixed Number Form:

$x = 4 \frac{1}{2}$

Solve for x 2*4^(x-3)=16

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