The value of y from the given expression is 6
Given the logarithmic function expressed as:
log3(y + 5) + log3 6 = log3 66
Accoding to the law of logarithm
log3(6(y++5)) = log3 66
The expression will become
6(y+5) = 66
6y + 30 = 66
6y = 66 - 30
6y = 36
y = 6
Hence the value of y from the given expression is 6
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Using the inverse of the logarithmic product property, it is found that the solution to the equation is y = 6.
It states that:
[tex]\log_{b}{MN} = \log_{b}{M} + \log_{b}{N}[/tex]
In this problem, the equation is:
[tex]\log_{3}{(y + 5)} + \log_{3}{6} = \log_{3}{66}[/tex]
Hence, applying the property:
[tex]\log_{3}{6(y + 5)} = \log_{3}{66}[/tex]
Logarithm function is injective, hence:
[tex]6(y + 5) = 66[/tex]
[tex]y + 5 = \frac{66}{6}[/tex]
[tex]y + 5 = 11[/tex]
[tex]y = 6[/tex]
Thus, it is found that the solution to the equation is y = 6.
More can be learned about logarithmic properties at https://brainly.com/question/25537936
