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Novosadov [1.4K]
4 years ago
13

How to solve

{y}(5y) = 2" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Natalija [7]4 years ago
5 0

Answer:

  y = 5

Step-by-step explanation:

Expand the logarithm:

\log_y{(5)}+\log_y{(y)}=2\\\\\dfrac{\log{(5)}}{\log{(y)}}+1=2 \quad\text{change of base formula}\\\\\dfrac{\log{(5)}}{\log{(y)}}=1 \quad\text{subtract 1}\\\\\log{(5)}=\log{(y)} \quad\text{multiply by log(y)}\\\\5=y \quad\text{take the anti-log}

_____

You can also take the antilog first:

  5y = y²

  y(y -5) = 0 . . . . . subtract 5y, factor

  y = 0 or 5 . . . . . y=0 is not a viable solution, so y=5.

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