Solve for b 5^7*5^b=5^3

$5^{7} \cdot 5^{b} = 5^{3}$

Step 1

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

$5^{7 + b} = 5^{3}$

Step 2

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

$7 + b = 3$

Step 3

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

Subtract $7$ from both sides of the equation.

$b = 3 - 7$

Subtract $7$ from $3$ .

$b = - 4$