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Math question on logarthms

Given that𝒛=𝟑𝒙𝟐
Show that 𝐥𝐨𝐠𝟑𝒛=𝐥𝐨𝐠𝟑𝟑𝒙𝟐
Please format the question properly using latex or appropiate use of the circumflex (^) for superscripts and underscores (_) for subscripts. As it stands the question is unreadable.
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Alinase
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Given that 𝒛 = 𝟑𝒙𝟐

Show that 𝐥𝐨𝐠𝟑 𝒛 = 𝐥𝐨𝐠𝟑 𝟑𝒙𝟐
Original post by NotNotBatman
Please format the question properly using latex or appropiate use of the circumflex (^) for superscripts and underscores (_) for subscripts. As it stands the question is unreadable.
Original post by Alinase
Given that 𝒛 = 𝟑𝒙𝟐

Show that 𝐥𝐨𝐠𝟑 𝒛 = 𝐥𝐨𝐠𝟑 𝟑𝒙𝟐


It still isn't clear, I'm afraid. I'm reading this as z=3x2 z=3x^2
Show that log(3)×z=log(3)×3x2 log(3) \times z = log(3) \times 3x^2

Which I don't think is the question as it's obvious, as it's comes from the first line.
Original post by Alinase
Given that 𝒛 = 𝟑𝒙𝟐

Show that 𝐥𝐨𝐠𝟑 𝒛 = 𝐥𝐨𝐠𝟑 𝟑𝒙𝟐


Assuming that you've written , log(3z)=log(3*3x2)

z = 3x2

z/2 = 3x

log(z/2)=log(3x)

log(z) - log(2) = log(3x)

log(z) = log(2) +log(3x) = log(3x2)

log(z) +log(3) = log(3x2) + log(3)

log(z) +log(3) = log(3z)

log(3x2) + log(3) = log(3*3x2)

so , log(3z) = log(3*3x2)


a bit long winded but I hope that makes sense

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