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Question

Solve the following equations for x:

(i) 72x+3=1

(ii) 2x+1=4x3

(iii)25x+3=8x+3

(iv) 42x=132

(v)4x1×(0.5)32x=(18)x

(vi)23x7=256

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Solution

(i) 72x+3=1 72x+3=702x+3=02x=3x=32

(ii) 2x+1=4x3 = 2x+1=(22)x32x+1=22x6Comparing, we getx+1=2x61+6=2xxx=7x=7

(iii)25x+3=8x+3

25x+3=(23)x+325x+3=23x+9Comparing, we get5x+3=3x+95x3x=932x=6x=62=3x=3

(iv) 42x=132 (22)2x=12524x=25Comparing, we get4x=5x=54x=54

(v)4x1×(0.5)32x=(18)x (22)x1×(12)32x=(123)x22x2×23+2x=23x22x23+2x=23x24x5=23xComparing, we get4x5=3x4x+3x=57x=5x=57x=57

(vi)23x7=256 = 23x7=28Comparing, we get3x=8+7=15x=153=5x=5


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