Log Equations Review OBJ: Review for Quest 2

Solve 1.162 – s 2 = ½ 24(2 – s 2) = 2-1 4(2 – s2) = -1 8 – 4s2 = -1 2.64x – 4 = (½)2x 26(x – 4 ) = (2-1)2x 6(x – 4) = (-1)2x 6x – 24 = -2x 8x = 24 x = 3

Solve 3.()2x = 64 4.63x + 5 = 1 60 = 1 ()2x = ()-3 3x + 5 = 0 27 ()2x = ()-3 2x = -3 x = -  4.63x + 5 = 1 60 = 1 3x + 5 = 0 x = -5 3

Solve 5.log5125 = x 5x = 125 5x = 53 x = 3 6.log2 t = 6 26 = t

Solve 7.log2x3 = 6 26 = x3 (26) = (x3) 22 = x 4 = x 8.log24 + log26= log2x log224 = log2x 24 = x

Solve 9log310-log35=log3x log310 = log3x 5 log32 = log3x 2 = x

Solve 11.log(x2 + 21x) = 2 (base 10) 102 = x2 + 21x 100 = x2 + 21x 12.2=log3(t2 – 3t + 5) 32 = t2 – 3t + 5 9 = t2 – 3t + 5 0 = t2 – 3t – 4 0 = (t – 4)(t + 1) t = 4, -1

Solve 132log23–log2(x + 1)=3 log2( 32 ) = 3 x+1 23 = ( 32 ) 8 = 9_ 8 = 9_ 8x + 8 = 9 8x = 1: x = ⅛ 14.log(x+5) – log(3x) = log(x+1) log(x+5) = log(x+1) 3x x + 5 = x + 1 3x2 +3x = x + 5 3x2 + 2x – 5 = 0 (3x + 5)(x – 1) = 0; x=1

Solve 15.log(n+4) =1–log(2n) ln(x + 1) – ln x = ln2 log10(n+4)(2n) = 1 101 = (n + 4)(2n) 2n2 + 8n – 10 = 0 2(n2 + 4n – 5) = 0 2(n + 5)(n – 1) = 0 n = 1 16.ln is the same as loge ln(x + 1) – ln x = ln2 ln x + 1 = ln2 x x + 1 = 2 2x = x + 1 x = 1

Solve. Round answers to 3 dec. places 17.2x = 5 log2x = log5 x log2 = log5 x = log5 log2 x = log(5)/log(2) x = 2.322 18.35 – x = 100 log35 – x = log100 (5 – x)log3 = log100 5log3-xlog3=log100 5log3-log100= xlog3 (5log(3)-log(100)) /log(3) x = .808

Solve. Round answers to 3 dec. places 19.log2x +1 = log31 – x (x + 1)log2 = (1 – x)log3 xlog2+1log2=1log3-xlog3 xlog2+xlog3 = log3–log2 x(log2+log3) = log3–log2 log3 – log2 = x log2 + log3 (log(3) – log(2))/(log(2) + log(3)) = x .226 = x

Solve. Round answers to 3 dec. places 20.ex = 4 log ex = log 4 x log e = log 4 x = log 4 log e x = 1.386 20.ex = 4 ln ex = ln4 x ln e = ln4 x = ln4 x = 1.386

Solve. Round answers to 3 dec. places 21.3e2x – 1 = 12 e2x – 1 = 4 log e2x – 1 = log 4 (2x – 1) log e = log4 2xlog e-log e = log4 x = log e + log 4 2 log e = 1.193 21.3e2x – 1 = 12 e2x – 1 = 4 ln e2x – 1 = ln4 2x – 1= ln4 2x = 1 + ln4 x = 1 + ln4 2 = 1.193

Solve. Round answers to 3 dec. places 21.3e2x – 1 = 12 e2x – 1 = 4 ln e2x – 1 = ln4 2x – 1= ln4 2x = 1 + ln4 x = 1 + ln4 2 = 1.193 22.72x + 1 = 11 log72x + 1 = log 11 (2x + 1)log7= log11 2xlog7+log7=log11 2xlog7=log11–log7 x = log11 – log7 2log7 x =

Solve. Round answers to 3 dec. places 23.log 5 x +3 = log 3 2 – x (x + 3)log5=(2 – x)log3 xlog5+3log5=2log3–xlog3 xlog5+xlog3=2log3–3log5 x(log5+log3)=2log3–3log5 2log3 – 3log5 = x log5 + log 3 -.972 = x 24.log2s = 1.3 21.3 = s 2.462 = s To do it on the calculator, type 2 Λ1.3 The “Λ” key is above the “” key

Solve. Round answers to 3 dec. places 25.log812 = x 8x = 12 xlog8 = log12 x = log12 log8 x = log(12)/log(8) x = 1.195 26.log53.6 = x 5x = 3.6 xlog5 = log3.6 x = log3.6 log5 x = log(3.6)/log(5) x = .796

Solve. Round answers to 3 dec. places 27.log1.26 = x 1.2x = 6 xlog1.2 = log6 x = log6 log1.2 x = 4.914 28.log27 = x x = 27 3-x = 3 x = -