A02 EEEEEEE question 15 (Marcellus working)

15) Find the exact value of x if (3x)^1g3 = (4x)^1g4

First, I add log to both sides.

lg (3x)^lg3 = lg (4x)^lg4

Then i will bring down the power

(lg3)(lg 3x) = (lg4)(lg 4x)

Expand

(lg3)^2+(lg3)(lgx) = (lg4)^2+(lg4)(lgx)

Change of subject

(lg3)^2-(lg4)^2 = (lg4)(lgx)-(lg3)(lgx)

Factorise

(lg3)^2-(lg4)^2 = (lgx)[(lg4)-(lg3)]

Change the subject of equation to (lgx)

lgx = [(lg3)^2-(lg4)^2]/[(lg4)-(lg3)]

Further simplify

lgx = -(lg3+lg4)

=-lg12

Remove lg from both sides

x = 12 ^(-1)
x=1/12 #