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UGH LOGS
Condense/Expand
Natural Logs
Solving Exponential Equations
Solving Logarithmic Equations
100

Solve for x: 4^(x - 5) = 12 

What is log(base4)12 + 5 ?

100

Expand ln (x^9)(y^5) 

9ln(x) + 5ln(y)

100

Solve: Ln (x - 5) = ln (2x - 11) 

What is x=6? 

100
Solve: 8^(2x)=8^(x+7)
What is x=7?
100
Solve: log(base 1/7)(7x+3)=log(base 1/7)(2x+13)
What is x=2
200

Solve: -6log(base3) (x-3)=-24 

What is x = 84?

200
Condense log2x+log3x-logx into one log expression.
What is log(6x)
200

Solve: -5ln (10x - 4) = -50

What is x = e^10 + 4 / 10

200
Solve: e^(2x)=e^(x+4)
What is x=4?
200

Solve: log (2x + 5) = 4

x = 9995/2 or 4997.5 

300

Solve for x: log(base8)2 + log(base8)4x^2 = 1

What is x = +1, -1? 

300

Expand ln(xy^1/3)

What is lnx + (1/3)lny

300
Solve: 2ln(x+3)=ln(13x+3)
What is x=6 and x=1.
300
Solve: 25^(x-4)=5^(3x+1)
What is x=-9 ?
300

Solve: 2log(base3)(4x-5) = 6

x = 8

400

log(base9)(x+6) - log(base9)x = log(base9)2 

What is x = 6? 

400

Condense log 15 + 5log x - 4log y

log (15x^5 / y^4) 

400

Solve: e^(-4x + 3) = 12

What is x=ln12 - 3 / -4

400

Solve 32^(x-2) = (1/4)^(3x)

x = 10/11

400
Solve: 2log(base 6)2=log(base 6)(4x+6)
What is x=-1/2.
500

Solve: ln(-3x-1) - ln 7 = 2

What is x = (-7e^2 - 1) / 3

500

Condense 5(log 2 + log x) - (log y + 2logz) 

What is log (32x^5)/(yz^2)

500
Solve for n: ln(n^2 + 12) = ln (-9n-2)

What is n = -2, -7?

500

Solve 5^(x-2) = 6^(2x+1)

x = (log 6 + 2log5) / (log 5 - 2log6) 

500

Solve: log (16+2b) = log b + log (b - 4) 

What is b = 8, -2 ?