Solve each of the following equations for X logx 18 3 log3

Solve each of the following equations for X. log_x (1/8) = 3 log_3 (3x - 2) = 2 log_b 36 = 5x + 3 e^-2x + 1 = 13 Human blood has a pH of 7.4. Find the hydronium concentration. What is the pH of a Solution for which the hydrogen ion concentration is 3.18 times 10^-4? A zero - level earthquake has a seismograph reading X_o of 10^-3 mm at a distance of 100 km from the epicenter and the Magnitude M(x) is given by M_(x) = log (X/X_o) where X is the seismograph reading. For the San Francisco earthquake of 1906, the seismograph reading 100 Km away was 50119 mm. What was the magnitude of this earthquake?

Solution

1)

a)log_x(1/8)=3

[since log_ab=c =>a^c=b ]

=>x³=1/8

=>x³=(1/2)³

=>x=1/2

b)log₃(3x-2)=2

[since log_ab=c =>b=a^c ]

(3x-2)=3²

(3x-2)=9

3x=9+2

3x=11

x=11/3

c)log₆36=5x+3

5x+3=log₆36

5x+3=log₆ 6²

[since log_aa^m=m*log_aa ]

5x+3=2log₆ 6

[since log_aa=1 ]

5x+3=2*1

5x+3=2

5x=-3+2

5x=-1

x=-1/5

d)e^-2x+1=13

[since e^a =b =>a=ln(b) ]

-2x+1=ln13

2x=(1-ln13)

x=(1/2)(1-ln13)