Math Review Game

Exponents to log

100

(1/5)^x=y

Log_(1/5)y=x

200

3³=27

Log₃27=3

300

4^-2=?

Log₄(1/16)=-2

400

12^(1/3)=?

x=1/1728

Log₁₂1/1728=1/3

500

6^-(2/3)=?

=0.3028 

Log₆(0.3028)=-(2/3) 

Log to Exponents

100

Log₃27=3

3³=27

200

log₂₁₆6=(1/3)

216^1/3=6

300

Log_(1/4)(1/64)=?

x=3

(1/4)³=(1/64)

400

Log₃(1/81)=?

= -4

3^-4=(1/81)

500

Log₂√2=?

=(1/2)

2^(01/2)=√2

Condensing

100

Log3+Log7+Log(1/2)=

Log(10.5) or Log(21/2)

200

log3+log4-log5−log6=?

log(12/30) or log(2/5)

300

20log₉8 - 4log₉11

Log₉(8²⁰/11⁴)

400

log₈7 + 1/3(log₈6) + 1/3(log₈5)

Log₈(7∛30)

500

2logx−4log(x+5)+(1/x)log(3x+5)

log((x²)(3x+5)^1/x)/(x+5)⁴

Expanding

100

Log₃ (10²/4)

2log₃10-log₃4

200

Log₅(x⁴z/y)

4log₅X+log₅Z-log₅Y

300

log(a²b³/c⁴d⁵)

2loga+3logb-4logc-5logd

400

log_9(ZY²)

log₉(z)+2log₉(y)

500

9log₁₀(9y²)+3²

log₁₀9⁹+log₁₀y¹⁸+9

Solve

100

3log₃4=log₃(x+10)

log₃64=log₃(x+10)

64=x+10

54=x

200

log₃X-log₃2=5

log₃(x/2)=5

3⁵=x/2

243=x/2

486=x

300

3.4e^2-2x-9=-4

3.4e^2-2x=5

e^2-2x=(5/3.4)

2-2x=LN(5/3.4)

-2x=Ln(5/3.4)-2

x=(LN(5/3.4)-2)/-2        or=0.80719876

400

6e^-4k-10-4=63

6e^-4k-10=67

e^-4k-10=67/6

-4k-10=ln(67/6)

-4k=ln(67/6)+10

k=(ln(67/6)+10)/-4 or x=-3.1032

500

10+4LogX = 4

4logx=-6

logx=-6/4

10^-6/4=x    or 0.031622=x