Warm Up Solutions

Solve for the variable.

$4^{8} = 4^{3} \cdot 4^{n}$

$8 = 3 + n n = 5$

Note

Q: When bases are multiplied, what operation happens to the exponents?

A: They are added.

$3^{12} = \frac{3^{z}}{3^{7}}$

$12 = z - 7 z = 19$

Note

Q: When bases are divided, what operation happens to the exponents?

A: They are subtracted.

Note

Problems 3–4

Use your Formula Sheet as a reference and review for the exponent properties and properties of logarithms.

$\sqrt[3]{25} = 5^{\frac{x}{3}}$

$\begin{array}{rcl} \sqrt[3]{5^{2}} & = & 5^{\frac{x}{3}} \\ 5^{\frac{2}{3}} & = & 5^{\frac{x}{3}} \\ \frac{2}{3} & = & \frac{x}{3} \\ x & = & 2 \end{array}$

$2^{24} = {(\frac{2^{9}}{2^{h}})}^{3}$

$\begin{array}{rcl} 2^{24} & = & \frac{2^{27}}{2^{3 h}} \\ 24 & = & 27 - 3 h \\ - 3 & = & - 3 h \\ h & = & 1 \end{array}$