Algebra - Evaluate Each Expression Assignment

Algebra Study Guide Evaluate each expression. 1) log₆ 36 6^x = 36 x = 2 2) log₃ 1/27 3^x = 1/27 x = -3 3) log₂ 32 2^x = 32 x = 5 4) log₇ 1/49 7^x = 1/49 x = -2 5) log₆ 64 6^x = 64 x = 2 6) log₆ 216 6^x = 216 x = 3 7) 4^x = 1/64 x = -3 8) log₈ 1 8^x = 1 x = 0 9) log₈ 8 8^x = 8 x = 1 10) log₇ 1 7^x = 1 x = 0 11) log₆ 1/36 6^x = 1/36 x = -2 12) log₄ 1/4 4^x = 1/4 x = -1/2 13) log₁₆ 1/2 16^x = 1/2 x = -1/4 14) log₄ -4 Undefined 15) log₅ 5 5^x = 5 x = 1 16) log₁₀ -25 Undefined 17) log₅ 125 5^x = 125 x = 3 18) log₈₁ 3 81^x = 3 x = 1/4 a) ln e^e e^x = e x = 1 b) ln e^-3 e^x = e^-3 x = -3 c) ln 1/e e^x = 1/e x = -1 d) ln 1 e^x = 1 x = 0 Rewrite each equation in exponential form. 19) log₁₄ 1 = 0 14⁰ = 1 20) log₂₅ 1/25 = -2 25⁻² = 1/25 21) log₁₂ 144 = 2 12² = 144 Rewrite each equation in logarithmic form. 22) 9² = 81 log₉ 81 = 2 23) 32⁴⁻¹ = 1/18 log₃₂₄ 1/18 = -1/2 24) 16² = 256 log₁₆ 256 = 2 Expand each logarithm. 25) log₃ (2/7²)⁵ log₃ 2⁵ - log₃ 7¹⁰ 5log₃ 2 - 10log₃ 7 26) log₃ (a·b·c²) log₃ a + log₃ b + log₃ c² log₃ a + log₃ b + 2log₃ c 27) log₅ (a³b⁴) log₅ a³ + log₅ b⁴ 3log₅ a + 4log₅ b Condense each expression to a single logarithm. 28) 3 ln x + 12 ln y ln x³y¹² 29) 5log₃ a - 30log₃ b log₃ a⁵/b³⁰ 30) log₇ x + log₇ y + 4log₇ z log₇ xyz⁴ **STUDY GUIDE (Cont'd)** 31. Evaluate the following: A. log₄ 256 64^x = 256 2^(6x) = 2^8 6x = 8 x = 4/3 B. log₂₇ 9 27^x = 9 3^(3x) = 3² 3x = 2 x = 2/3 C. log₂₅ 625 25^x = 625 5^(2x) = 5^4 2x = 4 x = 2 D. log₂ √8 2^x = √8 2^x = 8^(1/2) 2^x = 2^(3(1/2)) x = 1.5 E. log₄ 1/64 4^x = 1/64 x = -3 F. log 0.01 10^x = 0.01 x = -2