Number and Algebra
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Calculus
Simplify log3(7)+log3(5)\log_3(7) + \log_3(5)log3(7)+log3(5) to a single logarithm.
Simplify 2log2(x)−log2(8)2\log_2(x) - \log_2(8)2log2(x)−log2(8) to a single logarithm.
Simplify 3log10(2)+log10(25)3\log_{10}(2) + \log_{10}(25)3log10(2)+log10(25) to a single logarithm.
Simplify ln(a)−ln(b)+ln(c)\ln(a) - \ln(b) + \ln(c)ln(a)−ln(b)+ln(c) to a single logarithm.
Express log5(a3)+4log5(b)\log_5(a^3) + 4\log_5(b)log5(a3)+4log5(b) as a single logarithm.
Simplify ln(x)−3ln(y)+2ln(z)\ln(x) - 3\ln(y) + 2\ln(z)ln(x)−3ln(y)+2ln(z) to a single logarithm.
Combine log7(m)+log7(n)−log7(p)\log_7(m) + \log_7(n) - \log_7(p)log7(m)+log7(n)−log7(p) into a single logarithm.
Simplify log4(16x)−log4(2y)\log_4(16x) - \log_4(2y)log4(16x)−log4(2y) to a single logarithm.
Simplify log3(9)+log3(x2)−2log3(y)\log_3(9) + \log_3(x^2) - 2\log_3(y)log3(9)+log3(x2)−2log3(y) to a single logarithm.
Simplify log2(8)+log2(4)−3log2(x)\log_2(8) + \log_2(4) - 3\log_2(x)log2(8)+log2(4)−3log2(x) to a single logarithm.
Simplify logx(y)−4logx(2y)\log_x(y) - 4\log_x(2y)logx(y)−4logx(2y) to a single logarithm.
Express 5log5(x)−log5(x3y)5\log_5(x) - \log_5(x^3y)5log5(x)−log5(x3y) as a single logarithm.
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Question Type 4: Using laws of logarithms
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Question Type 6: Using logₐ(a) = 1 and logₐ(1) = 0