Solve for t using natural logarithms 5t 7 130 10t 2 102t

Solve for t using natural logarithms 5^t = 7 130 = 10^t 2 = (102)^t 10= 2^t 100 = 25(1.5)^t 50 = 10^(3^t) a = b^t 10 = e^t 5 = 2e^t e^34 = 100 10 = 6e^0.5t B = Pe^rt 2P = Pe^0.3t 7(3^t) = 5 (2^t) 5e^3t = 8w^2t For Exercises 2-16, solve for x using logs. 3^x = 11 17^x = 2 10 = 4^x 20 = 50(1.04)^x 25 = 2(5)^x 4 middot 3^x = 7 middot 5^x 2 middot 5^x = 11 middot 7^x 2^x = e^x + 1 7 = 5e^0.2x 50 = 600e^-0.4x 2e^3x = 4e^5x 7^x+2 = e^17x 10^x + 3 = 5e^7 - x 2x - 1 = e^9^x = 2e^x^3 For Exercises 17-22, solve for t. Assume a and b are positive constants and k is nonzero. a = b^t P = P_o a^t Q = Q_o b_t P = P_0

Solution

3.   5^t=7

Taking natural log that is Ln on both sides

Ln 5^t= Ln 7

t Ln 5= Ln 7

t= Ln7/Ln 5 = 1.21

4. 130 =10^t

Taking Ln on both sides

Ln 130 = Ln 10^t

Ln 130 = t Ln 10

t= Ln 130/Ln 10 = 2.11

5. 2= (1.02)^t

Ln 2 = Ln (1.02)^t

Ln 2= t Ln 1.02

t= Ln 2/Ln 1.02 = 35