Question-159345

Question Number 159345 by akolade last updated on 15/Nov/21

Answered by Ar Brandon last updated on 15/Nov/21

5^{\frac{y}{2} + 3} = 125 (5^{\frac{y}{2}}) = 125 {(5^{y})}^{\frac{1}{2}}

= 125 {(36)}^{\frac{1}{2}} = 125 \times 6 = 750

Commented by akolade last updated on 15/Nov/21

cool sir

Answered by yeti123 last updated on 16/Nov/21

5^{y} = 36

y = \log_{5} 36

x = 5^{\frac{y}{2} + 3}

\log_{5} x = \log_{5} (5^{\frac{y}{2} + 3})

= (\frac{y}{2} + 3) \log_{5} 5

= \frac{y}{2} + 3

= \frac{1}{2} \log_{5} 36 + 3

= \log_{5} 36^{1 / 2} + \log_{5} 5^{3}

= \log_{5} 6 + \log_{5} 125

= \log_{5} (6 \times 125)

x = 6 \times 125

= 750

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