Solving logs and properties

logax = y

100

log₂4 = ?

2

200

log₇1 = ?

0

300

log₅125 = ?

3

400

log₉3 = ?

1/2

with negatives

100

log₃(1/9) = ?

-2

200

log₄(1/64) = ?

-3

300

log₆(1/36) = ?

-2

400

log(1/10000) = ?

-4

one to one

100

log₄(x + 6) = log₄10

x = 4

200

log₃(x² + 8) = log₃72

x = +/- 8

300

log₂(5x + 1) = log₂(3x - 3)

x = -2

400

log(10 - 3x) = log(-4x)

x = -10

inverse properties

100

2^log₂(4x) = ?

4x

200

log₂(2⁸) = ?

8

300

8^log₈^3x= ?

3x

400

log₄(4^{7 + x}) = ?

7 + x

exponent form to log form

100

2⁴ = 16

log₂16 = 4

200

3⁴ = 81

log₃81 = 4

300

10⁴ = 10000

log₁₀10000 = 4

or

log10000 = 4

400

4⁵ = 1024

log₄1,024 = 5