Please show your work

Name: Answer all questions and show your work 1. Solve the following equations. (a) 57-1 = 1 125 (b) e3z-5 = 23 (c) ex?+2 = 3x (d) logg (x - 6) = log, 6 (e) ex = 8 (f) In(x2 - 3) =0 2. Describe any transformations of the graph of f that yield the graph of g. Sketch the graphs with y-intercepts and horizontal asymptotes. f (x) = 45, 9(2) = 45 +9 3. Find the domain, x-intercept, and vertical asymptote of the function and sketch the graph. y = In(x -3) +5 4. Find the exact value of the logarithmic expression without using a calculator. (a) 10g4 16 (b) log2 V16 (c) 4 1ne6 - Ine2 5. Expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.) (a) In((xy)?) (b) 10g7 () (c) In ( Vx2 + 3 6. Condense the expression to the logarithm of a single quantity. (a) log5 6 - logs t (b) 61n 2 - 8In(z - 3)