cms 2025-2026 nc math 4 initial credit (approved for wmhs spr 26)\nevaluating logarithmic expressions\nevalua…

cms 2025-2026 nc math 4 initial credit (approved for wmhs spr 26)\nevaluating logarithmic expressions\nevaluating logarithms\nevaluate: $\\log_{27} 9$\n$\\frac{2}{3}$\n$\\frac{3}{2}$\n$\\frac{1}{3}$\n$-\\frac{1}{3}$

cms 2025-2026 nc math 4 initial credit (approved for wmhs spr 26)\nevaluating logarithmic expressions\nevaluating logarithms\nevaluate: $\\log_{27} 9$\n$\\frac{2}{3}$\n$\\frac{3}{2}$\n$\\frac{1}{3}$\n$-\\frac{1}{3}$

Answer

Explanation:

Step1: Identify the logarithmic expression to evaluate

$$\log_{27} 9$$

Step2: Express the base and the argument as powers of 3

$$27 = 3^3, \quad 9 = 3^2$$

Step3: Substitute the power forms into the expression

$$\log_{3^3} (3^2)$$

Step4: Apply the change of base or power property

$$\frac{2}{3} \log_{3} 3$$

Step5: Simplify using the identity $\log_{b} b = 1$

$$\frac{2}{3} \times 1 = \frac{2}{3}$$

Answer:

$\frac{2}{3}$