Math, asked by study52, 10 months ago

log 3 root 3 to the base 27 is equal to X​

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Answered by ihrishi
6

Step-by-step explanation:

log_{27}3 \sqrt{3}  = x \\  \therefore \: 3 \sqrt{3}  =  {27}^{x}  \\ \therefore \: 3  \times  {3}^{ \frac{1}{2} }   =  {3}^{3x}  \\ \therefore \: {3}^{ 1 + \frac{1}{2} }   =  {3}^{3x}  \\ \therefore \: {3}^{ \frac{3}{2} }   =  {3}^{3x}  \\  \frac{3}{2}  = 3x \\  \implies \: x =  \frac{3}{2 \times 3} \\ \huge \purple{ \boxed{  \implies \: x =  \frac{1}{2} }}

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