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Question

Find the values of x in each of the following:

(i)25x÷2x=5220

(ii)(23)4=(22)x

(iii)(35)x(53)2x=12527

(iv)5x2×32x3=135

(v)2x7×5x4=1250

(vi)(34)2x+12=132

(vii)52x+3=1

(viii)   (13)x=44346

(ix)(35)x+1=12527


Solution

(i)25x÷2x=522025x2x=(220)1525xx=220524x=2205Comparing,we get4x=205x=205×4=1x=1

(ii)(23)4=(22)x23×4=22×x212=22xComparing,we get2x=12x=122=6x=6

(iii)(35)x(53)2x=12527(53)x(53)2x=5333(53)x+2x=(53)3Comparing,we getx+2x=3x=3x=3

(iv)5x2×32x3=1355x2×32x3=1355x.52.32x.33=1355x.32x52×33=1355x.32x=135×52×335x×3x×3x=135×25×27(5×3×3)x=3×3×3×5×5×5×3×3×3(45)x=(3×5×3)3=(45)3Comparing,we getx=3

(v)2x7×5x4=12502x7×5x4=12502x.27.5x.54=2×5×5×5×52x.5x27×54=2×5×5×5×5(10)x=2×5×5×5×5×2×2×2×2×2×2×2×5×5×5×5(10)x=28×58=(10)8Comparing,we getx=8

(vi)(34)2x+12=132[(22)13]2x+12=125223(2x+12)=2523(2x+12)=543x+13=58x+2=5×68x=302x=328=4

(vii)52x+3=1=50(a0=1)2x+3=02x=3x=32

(viii)   (13)x=44346=256816=169=(13)2x=2Squaring,x=4

(ix)(35)x+1=12527(35)x+12=(35)3          {am=1am}x+12=3x+1=6x=7x=7


Mathematics
RD Sharma
Standard IX

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