Question

Solve : 3^2x+1÷ 9 =27

Answer 1

Answer:

The solution of the given expression is at x=1.495.

Step-by-step explanation:

Given : Expression $3^{2x}+\frac{1}{9}=27$

To find : Solve the expression ?

Solution :

Expression $3^{2x}+\frac{1}{9}=27$

Taking 1/9 to other side,

$3^{2x}=27-\frac{1}{9}$

$3^{2x}=\frac{243-1}{9}$

$3^{2x}=\frac{242}{9}$

Taking log both side,

$2x\log 3=\log(\frac{242}{9})$

$2x=\frac{\log(\frac{242}{9})}{\log 3}$

$2x=2.99$

$x=\farc{2.99}{2}$

$x=1.495$

Therefore, The solution of the given expression is at x=1.495.

Answer 2

Answer:

$Value \: of \: x = 2$

Step-by-step explanation:

$Given \: 3^{2x+1}\div 9 = 27$

$\implies 3^{2x+1}=27 \times 9$

$\implies 3^{2x+1}=3^{3} \times 3^{2}$

$\implies 3^{2x+1}=3^{3+2}$

$\implies 3^{2x+1}=3^{5}$

$\implies 2x+1 = 5$

$We \: know \: the \\</p><p>exponential \:law:\\</p><p>If \: a^{m}=a^{n}\: then \:m=n$

$\implies 2x=5-1$

$\implies 2x = 4$

$\implies x =\frac{4}{2}$

$\implies x = 2$

Therefore,

$Value \: of \: x = 2$

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