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  text: '[summary:\n\n- [ Inversion of exponentials]: $b^{\\log_b(n)} = \\log_b(b^n) = n.$\n- [ Log of 1 is 0]: $\\log_b(1) = 0$\n- [ Log of the base is 1]: $\\log_b(b) = 1$\n- [ Multiplication is addition in logspace]: $\\log_b(x\\cdot y) = log_b(x) + \\log_b(y).$\n- [ Exponentiation is multiplication in logspace]: $\\log_b(x^n) = n\\log_b(x).$\n- [ Symmetry across log exponents]: $x^{\\log_b(y)} = y^{\\log_b(x)}.$\n- [ Change of base]: $\\log_b(n) = \\frac{\\log_a(n)}{\\log_a(b)}$]\n\nRecall that [3nd $\\log_b(n)$] is defined to be the (possibly fractional) number of times that you have to multiply 1 by $b$ to get $n.$ Logarithm functions  satisfy the following properties, for any base $b$:\n\n- [ Inversion of exponentials]: $b^{\\log_b(n)} = \\log_b(b^n) = n.$\n- [ Log of 1 is 0]: $\\log_b(1) = 0$\n- [ Log of the base is 1]: $\\log_b(b) = 1$\n- [ Multiplication is addition in logspace]: $\\log_b(x\\cdot y) = log_b(x) + \\log_b(y).$\n- [ Exponentiation is multiplication in logspace]: $\\log_b(x^n) = n\\log_b(x).$\n- [ Symmetry across log exponents]: $x^{\\log_b(y)} = y^{\\log_b(x)}.$\n- [ Change of base]: $\\log_a(n) = \\frac{\\log_b(n)}{\\log_b(a)}$',
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