Log expansion and condensing

Multiply

100

 log2xy

log2 + logx +logy

200

log4 + 6logx + logy

log4(x^6y)

300

How do you make sure you have fully expanded correctly?

You must have log written more than one time, You have to have at least one addition or subtraction sign, there can be no multiplication or division and all exponents have been brought to the front.

400

In3 + Inx

In3x

500

log₃10 + log₃8

log₃80

Division

100

ln10/x

ln10-lnx

200

log₉(h⁶/f⁸k³⁾

6log₉h - 8log₉f - 3log₉k

300

log15-log3

5

400

logx - 5logy - 3log(z + 3)

logx - logy⁵ - log(z+3)⁵

500

log₄96 - log₄6

4

Exponents

100

logx⁵

5logx

200

10logh

logh¹⁰

300

4lnx

lnx⁴

400

log10 + 8^{log8 26} - log100

1 + 26 - 2 = 25

500

log5x + 2^{log2 x} - log20x

log1/5 + x