Exponential and Logarithmic Functions Do Now 2

Write as the sum or difference of logarithms with no exponents log a x 4 y 3 4log a x – 3log a y log a 6 d 7 c 9 b 3 6loga + 7logd – 9logc –3logb

Write as the sum or difference of logarithms with no exponents log √x y ½ logx – logy log x 4 ∛ y 3 z 2 1/3(4logx –3logy –2logz)

Write as a single logarithm log 25 + log 4 (Hint base 10) log (25 4) log = x 10 x = x = 10 2 x = 2 3 log x + log y log x 3 y

Write as a single logarithm 6(log a + log b) log (ab) 6 9log t + 4log u log t 9 u 4

Write as a single logarithm 4log w + 4log u + 5log v log w 4 u 4 v 5 8log t – 4log s + 7log v log t 8 v 7 s 4

Write as a single logarithm log log 8 2 (Hint: make single logarithm = x and convert to exponential form to solve for x.) log = x log 8 8 = x 8 x = 8 8 x = 8 1 x = 1 2 log a x + 5 log a z – log a 2 – 3 log a y log a x 2 z 5 2y 3

Write as a single logarithm 8 log b t – 3 log b u – log b 6 – 2 log b s log b t 8 __ 6u 3 s 2 log a 2x + 3(log a x–log a y) log a 2x(x/y) 3 log a 2x x 3 y 3 log a 2x 4 y 3

Solve 2 x =  2 x = 2 -4 x = x – 4 = (½) 2x 2 6(x – 4) = 2 -1(2x) 6x – 24 = -2x 8x = 24 x = 3

Solve (¾) 2x = (¾) 2x = (¾) 2x = (¾) -3 2x = -3 x = -3/2 e 3x = e 7x – 2 3x = 7x – 2 -4x = -2 x = ½

Solve log n 1 = 2 25 n 2 = 1 25 n 2 = (1) 2 (5) n = 1 5 log √2 t = 6  2 6 = t  64 = t 8 = t OR 2 6(1/2) = t 2 3 = t 8 = t

Solve log 2 x 3 = = x 3 64 = x = x 3 4 = x OR (2 6 ) 1/3 = (x 3 ) 1/3 2 2 = x 4 = x ln (3x – 5) = 0 log e (3x – 5) = 0 e 0 = (3x – 5) 1 = 3x – 5 6 = 3x 2 = x