Question 9 Evaluate Given that logx 5 and log y 4 find log

Question 9 Evaluate. Given that logx 5 and log y - 4, find log xy4 21 O 1280 O36 O 80 Question 10 Solve the logarithmic equation. log3(x + 2) + log3(x 2) 1 Question 11 Use the change-of-base formula and a calculator to evaluate each logarithm. log s 157.4 O 0.4515 2.4328

Solution

9. log x= 5 ; (log y= 4 )×4 -> 4 log y= 16

4 log y= log y⁴=16

log x+log y⁴=log (xy⁴)= 5+16=21

10. log₃(x+2)+log₃ (x-2)=11

log₃( (x-2)(x+2))=1

(x-2)(x+2)=3¹

x²-4=3

x=(7)^1/2

11. log _8^1/2 (157.4)= log (157.4)/log (8)^1/2

12. log₅1=0

5⁰=1

13. ln28= log_e28= 3.3322

28= e^3.3322