Properties of Logarithmic Functions

log(base7)49=2

Change 49=7^2 into logarithmic form.

log(base5)625=4

Change 625=5^4 into logarithmic form.

3²=9

Change log(base 3)9=2 into exponential form.

4³=64

Change log(base 4)64=3 into exponential form.

ln3+lnx+lny

Expand ln(3xy)

log2+logx+2log y

Expand log(2xy²)

2logx-logy

Expand log(x²/y)

log x - 6log y

Expand, using the properties of logs.

2log x + 2 log y

Expand, using the properties of logs. log(x²)(y²)

4log x + log y

Expand, using the properties of logs. log(x⁴)(y)

4log x - log y

Expand, using the properties of logs. logx⁴/y

log (2x)^(3y)

Write 2log2x+log3y as a single log term.

log64

Write 2log8 as a single log term.

log 32

Write 2log8-log2 as a single log term.

ln(x/y⁴)

Write as a single logarithm.

log (2x)(3y)

Write log2x+log3y as a single log term.

log 2x/3y

Write log2x-log3y as a single log term.

log 16

Write log8+log2 as a single log term.

log 4

Write log8-log2 as a single log term.

log(xy³)

Write logx+3log y as a single log term.

log(x/y)

Write logx-logy as a single log term.

log 128

Write2log8+log2 as a single log term.