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Laws of Logarithms (Grades 11-12)

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Laws of Logarithms

Instructions: Assume that all variables are positive.

1. 
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]
2. 
Expand [math]log (7/5)^6[/math] using the Laws of Logarithms.
  1. [math]log 7 + log 5[/math]
  2. [math]6log7 - 6log5[/math]
  3. [math]log 7 - log 5[/math]
  4. [math]6log 7 - 6log 5[/math]
3. 
Expand [math]log_2 (6^5* 8^4)[/math] using the Laws of Logarithms.
  1. [math]5log_2 6+log_2 8^4[/math]
  2. [math]log_2 6^5+log_2 8^4[/math]
  3. [math]5log_2 6+ 4log_2 8[/math]
  4. [math]log_2 6^5+ 4log_2 8[/math]
4. 
Expand [math]log_4 (2*11*7^4)[/math] using the Laws of Logarithms.
  1. [math]log_4 2- log_4 11-log_4 7^4[/math]
  2. [math]log_4 2+ log_4 11+4log_4 7[/math]
  3. [math]log_4 2- log_4 11-4log_4 7[/math]
  4. [math]log_4 2+ log_4 11+ log_4 7^4[/math]
5. 
Simplify the expression [math] log 100^x [/math].
  1. [math]2[/math]
  2. [math]x[/math]
  3. [math]2x[/math]
  4. [math]2^x[/math]
6. 
Expand [math]log_14 (d^4/s^2)[/math] using the Laws of Logarithms.
  1. [math]log_14 d^4 - log_14 s^2[/math]
  2. [math]log_14 d^4 - 2log_14 s[/math]
  3. [math]4log_14 d - log_14 s^2[/math]
  4. [math]4log_14 d - 2log_14 s[/math]
7. 
Simplify the expression. [math]4^(log_4 16x)[/math]
  1. [math]2x[/math]
  2. [math]16x[/math]
  3. [math]4^(2x)[/math]
  4. [math]log 16x[/math]
8. 
Expand [math]log_15 k^6root8(m)[/math] using the Laws of Logarithms.
  1. [math]6log_15 k + log_15 m[/math]
  2. [math]log_15 k + 1/8log_15 m[/math]
  3. [math]6log_15 k + 1/8log_15 m[/math]
  4. [math]log_15 k + log_15 m[/math]
9. 
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]
10. 
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]
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