Question

Solve the equation by expressing each side as a power of the same base and then equating exponents. Solve the exponential equation. Express the solution set in terms of natural logarithms. 1)20x-5)=16 4)385 x + Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic xp ressions Give the exact answer. 2)ex + 5- 5) 10g4 x + log4( 15)-2

Answer 1

2^(3x - 5) = 16 16 = (2) ^4 2^(3x - 5) = (2) ^4 Since base is same, using a^x = a^y implies x = y 3x - 5 = 4 3x = 4 + 5 3x = 9 x = 9/3 x = 3 e^x + 5 = e^1/9 using a^-1 = 1/a e^x + 5 e^-9 Since bases are same x + 5 = -9 x = -9-5 x = -14