Question 1
Solve the equation, log3 [log2(2x – 1)] = 2
Solution:
log3 [log2 (2x – 1)] = 2 ← (if log a N = x, N = ax)
log2 (2x – 1) = 32
log2 (2x – 1) = 9
log2 (2x – 1) = 9
2x – 1 = 29
x = 256.5
Question 2
Solve the equation,
log16[log2(5x– 4)]=log9√3
Solution:
log16[log2(5x– 4)]=log9√3log16[log2(5x– 4)]=14←log9√3=log9312=12log93=12(1log39)=12(12)=14log2(5x– 4)=1614log2(5x– 4)=25x– 4=225x=8x=85
Question 3
Solve the equation,
5log4x=125
Solution:
5log4x=125log55log4x=log5125←put log for both side(log4x)(log55)=3(log4x)(1)=3x=43=64
Question 4
Solve the equation,
5log5(x+1)=9
Solution:
5log5(x+1)=9log55log5(x+1)=log59log5(x+1).log55=log59log5(x+1)=log59x+1=9x=8