Solve the following equations: (i)3x+1=27×34(ii)42x=(3√16)−6y=(�

1.	Solve the following equations: (i)3x+1=27×34(ii)42x=(3√16)−6y=(√8)2(iii)3x−1×52y−3=225(iv)8x+1=16y+2 and (12)3+x=(14)3y(v)4x−1×(0.5)3−2x=(18)x(vi)√ab=(ba)1−2x,where a,b are distinct positive primes.
Answer» Solve the following equations: $(i) 3^{x + 1} = 27 \times 3^{4} (i i) 4^{2 x} = (\sqrt[3]{16})^{\frac{- 6}{y}} = (\sqrt{8})^{2} (i i i) 3^{x - 1} \times 5^{2 y - 3} = 225 (i v) 8^{x + 1} = 16^{y + 2} a n d {(\frac{1}{2})}^{3 + x} = {(\frac{1}{4})}^{3 y} (v) 4^{x - 1} \times (0.5)^{3 - 2 x} = {(\frac{1}{8})}^{x} (v i) \sqrt{\frac{a}{b}} = {(\frac{b}{a})}^{1 - 2 x}, w h e r e a, b a r e d i s t i n c t p o s i t i v e p r i m e s .$

Solve the following equations: (i)3x+1=27×34(ii)42x=(3√16)−6y=(√8)2(iii)3x−1×52y−3=225(iv)8x+1=16y+2 and (12)3+x=(14)3y(v)4x−1×(0.5)3−2x=(18)x(vi)√ab=(ba)1−2x,where a,b are distinct positive primes.

Answer»

Solve the following equations:

$(i) 3^{x + 1} = 27 \times 3^{4} (i i) 4^{2 x} = (\sqrt[3]{16})^{\frac{- 6}{y}} = (\sqrt{8})^{2} (i i i) 3^{x - 1} \times 5^{2 y - 3} = 225 (i v) 8^{x + 1} = 16^{y + 2} a n d {(\frac{1}{2})}^{3 + x} = {(\frac{1}{4})}^{3 y} (v) 4^{x - 1} \times (0.5)^{3 - 2 x} = {(\frac{1}{8})}^{x} (v i) \sqrt{\frac{a}{b}} = {(\frac{b}{a})}^{1 - 2 x}, w h e r e a, b a r e d i s t i n c t p o s i t i v e p r i m e s .$

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Solve the following equations: (i)3x+1=27×34(ii)42x=(3√16)−6y=(√8)2(iii)3x−1×52y−3=225(iv)8x+1=16y+2 and (12)3+x=(14)3y(v)4x−1×(0.5)3−2x=(18)x(vi)√ab=(ba)1−2x,where a,b are distinct positive primes.

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