7 Solve each equation GIVE EXACT ANSWERS no decimals a log x

7) Solve each equation. GIVE EXACT ANSWERS (no decimals.                                                              

a) log   x = - 3   d) log _x 5= 1/3   

b) log _x 1/11 = 1/2                                                                                 e) log7/3 9/49=x

c) log ₈ x = -3/2 f) e ^{ln 13}   = x

Solution

7.a    log x=-3

We have to use the following property

If log a=b,then   a=10^b

Therefore we get

x=10^-3=1/1000

b. log_x(1/11)=1/2

1/11 =x^1/2

x=1/121

logx=11/2

x=10^11/2

c. log₈x=-3/2

x= 8^-3/2

d.log_x5=1/3

5=x^1/3

x=5³=125

e.log_7/3(9/49)=x

9/49= (7/3)^x

(7/3)^-2=(7/3)^xx=-2

f.   e^{ln 13}=x

     x=13