IB Math SL Logarithms

Here you will find original IB Math SL exam style logarithms and exponential functions practice problems. Visit this page directly at hunkim.com/sllogarithms

  1. Evaluate as an integer:
    1. \log_4 4
    2. \log_4 2+\log_4 32
    3. \log_4 8-\log_4 2
  2. Evaluate \log_4 8
  3. Let a=\ln 3 and b=\ln 12. Write down the following expressions in terms of a and b:
    1. \ln 36
    2. \ln 4
    3. \ln 108
  4. Let p=\log_3 a, q=\log_3 b, and r=\log_3 c. Express the following in terms of p, q, and r:
    1. \log_3 \left(\frac{c}{ab}\right)
    2. \log_3 \left(\frac{a}{b^2c}\right)
    3. \log_b a
  5. Consider a=\log_{63} 64\times \log_{62} 63\times \log_{61} 62\times ...\times \log_2 3. Given that a\in\mathbb{Z}, find the value of a
  6. Solve \log_5 x-\log_5 2=1+\log_5 3
  7. Given that \log_b 3=7
    1. Find the exact value of \log_b 27
    2. Find the exact value of \log_{\sqrt{b}} 3
    3. Find the value of b, accurate to 3 significant figures
  8. Solve 125^{x+3}=\left(\frac{1}{25}\right)^{3x-2}
    1. Write down the value of:
      1. \log_3 27
      2. \log_2 \left(\frac{1}{4}\right)
      3. \log_{25} 5
    2. Hence solve \log_3 27+\log_2 \left(\frac{1}{4}\right)+\log_9 x
  10. Let q=\log_3 b. Express the following in terms of q:
    1. \log_3 b^2
    2. \log_3 27b
    3. \log_{27} b
    1. Write the expression 6\ln 2-\ln 8 in the form \ln a, where a\in\mathbb{Z}
    2. Hence, or otherwise, solve 6\ln 2-\ln 8=-\ln x
  12. Solve \log_3(x^2-4x+4)=1+\log_3(x-2)
  13. Solve \log_3(1-x)=\log_9(5-2x)
  14. Find the value of:
    1. \log_5 50-\log_5 2
    2. 25^{\log_5 6}
  15. Simplify e^{2\ln 3}
  16. Solve 4^x+3(2^{x+1})=2
  17. f(x)=\log_k (4x-6x^2). The equation f(x)=2 has exactly one solution. Find k
  18. 21^{2x}=81^{x-1}. Solve x in terms of \ln 3 and \ln 7
  19. Find integers a and b given a+\frac{b}{2}\log_8 7+10\log_2 14=0