Question

Tìm x biết

a)5^x+2=625

b)\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}...\frac{30}{62}.\frac{31}{64}=2^x\)

 

Answer 1

a)5^x+2=625

<=>5^x+2=5⁴

<=>x+2=4

<=>x=2

Answer 2

b)

 \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}....\frac{30}{62}.\frac{31}{64}=2^x\)

  \(\frac{1.2.3.4.....30.31}{4.6.8.10....62.64}=2^x\)

 \(\frac{1.2.3.4.5....30.31}{2.2.2.3.2.4.2.5.....2.31.64}=2^x\)

 \(\frac{1.2.3.4.5.....30.31}{\left(2.2.2....2.2\right).\left(2.3.4.5....30.31\right).64}=2^x\)

 \(2.2.2.2.2.....2.64=2^x\)

 \(2^{31}.2^6=2^x\)

\(2^{37}=2^x\)

=> \(x=37\)

Answer 3

a)5^x+2=625

<=>5^x+2=5⁴

<=>x+2=4

<=>x=2

Answer 4

a)5^x+2=625

<=>5^x+2=5⁴

<=>x+2=4

<=>x=2

Answer 5

\(\text{a)5x+2=625 }\)

<=>5^x+2=5⁴

<=>x+2=4

<=>x=2