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Logarithms Questions - All Grades

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Grade 10 Logarithms CCSS: HSF-BF.B.5
Write [math]64 ^(1/2) = 8[/math] in logarithmic form.
  1. [math]log_64 (1/2) =8[/math]
  2. [math]log_(1/2) 8 =64[/math]
  3. [math]log_64 8 = 1/2[/math]
  4. [math]log_(1/2) 64 =8[/math]
Grade 10 Logarithms CCSS: HSF-BF.B.5
Write [math]log_2 8 = 3[/math] in exponential form.
  1. [math]2^4 = 8[/math]
  2. [math]2^3 = 8[/math]
  3. [math]2^2 = 8[/math]
  4. [math]2^5 = 8[/math]
Grade 10 Logarithms CCSS: HSF-BF.B.5
[math]2^3=8[/math] is equivalent to which of the following?
  1. [math]log_8 2=3[/math]
  2. [math]log_3 8=2[/math]
  3. [math]log_2 8=3[/math]
  4. [math]log_8 3=2[/math]
Grade 11 Logarithms CCSS: HSF-BF.B.5, HSF-LE.A.4
[math]2^x=64[/math] is equivalent to which of the following?
  1. [math]log_64 x=2[/math]
  2. [math]log_2 64=x[/math]
  3. [math]log_2 x=64[/math]
  4. [math]log_x 64=2[/math]
Grade 10 Logarithms CCSS: HSF-IF.A.1
What is the domain of the function [math]f(x)=3log_2 x ?[/math]
  1. [math][0,oo)[/math]
  2. [math](0,oo)[/math]
  3. [math](3,oo)[/math]
  4. [math][2,oo)[/math]
  5. [math](-oo,oo)[/math]
Grade 9 Logarithms CCSS: HSF-BF.B.5
Which of the following expresses the equation in correct exponential form?

[math]log_10 0.0001=-4[/math]
  1. [math]10^-3=0.001[/math]
  2. [math]10^-4=0.0001[/math]
  3. [math]10xx10^-3=0.01[/math]
  4. [math]10xx10^-4=0.001[/math]
Grade 11 Logarithms CCSS: HSF-BF.B.5
[math]6^4=1296[/math] is equivalent to which of the following?
  1. [math]log_6 1296=4[/math]
  2. [math]log_4 1296=6[/math]
  3. [math]log_1296 6=3[/math]
  4. [math]log_6 4=1296[/math]
Grade 11 Logarithms
Express as a single logarithm. [math]2log(x) - 5log(y) + 3log(z)[/math]
  1. [math]log((x^2 z^3)/y^5)[/math]
  2. [math] -30log(xyz) [/math]
  3. [math] -log(x^2 y^5 z^3) [/math]
  4. [math] log((x^2 y^5)/z^3)[/math]
Grade 11 Logarithms
Express as a single logarithm. [math]3log a - 2log b - 4logc[/math]
  1. [math] log (3a - 2b - 4c)[/math]
  2. [math]log (a^3 - b^2 - c^4)[/math]
  3. [math]3log a - 2log b - 4logc[/math]
  4. [math]log ((a^3)/(b^2c^4))[/math]
  5. none of these are correct
Grade 11 Logarithms CCSS: HSF-BF.B.5
[math]4^x=256[/math] is equivalent to which of the following?
  1. [math]log_256 x=4[/math]
  2. [math]log_4 x=256[/math]
  3. [math]log_256 4=x[/math]
  4. [math]log_4 256=x[/math]
Grade 11 Logarithms CCSS: HSF-BF.B.5
Solve the logarithmic equation.

[math]5 log(x-2)=11[/math]
  1. [math]x=160.5[/math]
  2. [math]x=158.5[/math]
  3. [math]x=2.2[/math]
  4. [math]x=0.34[/math]
  5. [math]x=2.34[/math]
Grade 10 Logarithms CCSS: HSF-BF.B.5
Solve. [math]log_4 x- log_4 5= log_4 60[/math]
  1. 3
  2. 12
  3. 120
  4. 300
Grade 11 Logarithms
Expand [math]log (6*10)[/math] using the Laws of Logarithms.
  1. [math]log 6 + log 10[/math]
  2. [math]log 6 - log 10[/math]
  3. [math]log 60[/math]
  4. [math]log 6 /log 10[/math]
Grade 9 Logarithms CCSS: HSF-BF.B.5
Which of the following correctly expresses the equation in logarithmic form?

[math]2^6=64[/math]
  1. [math]log_6 2=64[/math]
  2. [math]log_2 6=64[/math]
  3. [math]log_6 64=2[/math]
  4. [math]log_2 64=6[/math]
Grade 11 Logarithms CCSS: HSF-BF.B.5
Write [math]4^2 = x[/math] in logarithmic form.
  1. [math]log_x4=2[/math]
  2. [math]log_4x=2[/math]
  3. [math]log_x2=4[/math]
  4. [math]log_4 2=x[/math]
Grade 11 Logarithms
Condense the logarithmic expression [math]log_5 a + log_5 b[/math] using the Laws of Logarithms.
  1. [math]log_5(a/b)[/math]
  2. [math]b log_5 a[/math]
  3. [math]log_5 (a*b)[/math]
  4. [math]log_a (5*b)[/math]
Grade 11 Logarithms CCSS: HSF-BF.B.5
Solve: [math]log_4(2y+2)-log_4(y-2)=1[/math]
  1. -5
  2. 5, 1
  3. 5
  4. No solution
Grade 11 Logarithms
Condense the logarithmic expression [math]log 4 - log 8[/math] using the laws of logarithms.
  1. [math]log (4*8)[/math]
  2. [math]log (4/8)[/math]
  3. [math]log 32[/math]
  4. [math]log 4+log8[/math]
Grade 11 Logarithms CCSS: HSF-BF.B.5
Write [math]5^3=125[/math] in logarithmic form.
  1. [math]log_3 125 = 5[/math]
  2. [math]log_5 3 = 125[/math]
  3. [math]log_3 5 = 125[/math]
  4. [math]log_5 125 = 3[/math]
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