Subjects algebra

Exponent Logarithm 00C7E6

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Simplify the expression $5^{1 - \log_5 3}$. 2. **Recall the properties of logarithms and exponents:** - The logarithm base 5 of 3 is $\log_5 3$. - The exponent rule: $a^{m-n} = \frac{a^m}{a^n}$. 3. **Rewrite the expression using the exponent rule:** $$5^{1 - \log_5 3} = \frac{5^1}{5^{\log_5 3}}$$ 4. **Simplify the denominator:** Since $5^{\log_5 3} = 3$ (because $a^{\log_a b} = b$), we have: $$\frac{5}{3}$$ 5. **Final answer:** The expression simplifies to $\frac{5}{3}$. Therefore, the correct choice is A. 5/3.