math

log formula

100

log₄(9)=x

round to the nearest thousandth

x=1.585

200

8^x=10

round to the nearest thousandth, and give an exact solution as a logarithm

log(10)/log(8)=x

x=1.107

300

In(3)=x

round to the nearest thousandth

x=1.099

400

3^x=4

round to the nearest thousandth, and give an exact solution as a logarithm

log (4)/log (3) =x

x=1.262

500

log₆(5)=x

round to the nearest thousandth

x=0.898

condensing

100

9 In x - 6 In y

In (x⁹/y⁶)

200

log₅6 + 1/2 log₅y

log₅(6√y)

300

2 log 10 + 4 log 3x

log (8100x⁴)

400

1/3 In 27 - 3 In (2y)

In 3√27 / (2y)³

500

1/2 log₉(x) - log₉(y) - 3 log₉(x)

log₉  √x/yz³

expanding

100

log₅ (2/3)

log₅ (2) - log₅ (3)

200

In 2x⁵

In(2) + 5 In(x)

300

log₆(2m⁵n³⁾

log₆ (2) + 5log₆(m) + 3log₆(n)

400

log₂(x/5y)

log₂(x) - log₂(5y)

500

log (a⁷b/√c)

7 log a + log b - 1/2 log c

formulas

100

what is the compound continuously formula?

A= Pe^rt

200

what is the appreciation/depreciation formula?

A(t)=P(1±r)^t

300

what is the compound interest formula?

A= P(1 + r/n)^nt

400

what is the change of base formula?

log_bm=log_am / log_ab

500

what is the quadratic formula?

x = (-b ± √(b² - 4ac)) / 2a

solve

100

2^x-4=16

x=8

200

5^3-2x=5^-x

x=3

300

144^2x+1=12^5x-1

x=3

400

e^6x-4=e^-2x+12

x=2

500

(1/2)^x+7=4^3x

x=-1