University:
Missouri State University
Course:
MTH 136 | Precalculus 1
Academic year:

2023
Views:

370

Pages:

18
Author:

nomphethofou

WARM-UP DIRECTIONS: Solve for x. Round to the nearest ten-thousandth. 7 ^ (x + 5) = 3 ^ (4x) x+5 4x ln(7) - ln(3) (x + 5) * ln(7) = 4x * ln(3) X ln 7+\ ln(7) = 4 * ln(3) -4x^3-517-4x/m3-5m7 Xln7-4x1n3=-51n7 x/n7-4x1n3=-5177 x(ln(7) - 4 * ln(3)) = - 5 * ln(7) x(ln(7) - ln(3 ^ 4)) =ln7 1 6 ^ -5 x(ln(7) - ln(81)) = ln(1/(7 ^ 5)) x * ln(7/81) = ln(1/6807) x = (ln(1/1625))/(ln(7/81)) X = 3.9736 SECTION 6 WORKSHEET - ANSWERS 1.) b \approx 2.5789 2.) r \approx 1.0322 3.) a \approx 3.854 4.) r \approx 2.1944 5.) x \approx 0.0951 6.) x \approx 3.3026 7.) n \approx - 8.0172 8.) n \approx 9.7005 9.) n \approx 8.062 10.) n \approx - 0.2165 EXAMPLE 5 Solving Logarithmic Equations log_2(x) + log_2(x + 2) = log_2(x + 6) Condense First log_2(x + 2x) = log_2(x + 6) x+3=0 -3-3 x-2=12 +2+2 x=2 x ^ alpha + 2x = x + 6 -6 X²+x-6= 0 2 (x + 3)(x - 2) = 0 9- X- Extraneous EXAMPLE 7 Solving Logarithmic Equations log_2(x) + log_2(x - 8) = 2 log_2(x ^ 2 - 8x) = 2 Q ^ 2 = x ^ 2 - 8x 4 = x - 8x O= x²-8x-4 Condense First! O = x ^ 2 - 8x - 4 Cant Factor 8 pm sqrt (- 8) ^ 2 - 40x - 4 ) 2(1) (8 plus/minus sqrt(64 + 16))/2 = (8 plus/minus sqrt(80))/2 = (8 plus/minus 4 * sqrt(5))/2 4 + 2sqrt(5) 4215 Extraneous