Number and Algebra
Functions
Geometry and Trigonometry
Statistics and Probability
Calculus
Simplify the expression loga(x)+2loga(y)−loga(z)\log_a(x) + 2\log_a(y) - \log_a(z)loga(x)+2loga(y)−loga(z) into a single logarithm.
Simplify log5(25)+3log5(2)−log5(4)\log_5(25)+3\log_5(2)-\log_5(4)log5(25)+3log5(2)−log5(4) into a single logarithm.
Simplify 2log7(14)−log7(2)2\log_7(14)-\log_7(2)2log7(14)−log7(2) into a single logarithm.
Simplify 3log3(2)−2log3(5)3\log_3(2)-2\log_3(5)3log3(2)−2log3(5) into a single logarithm.
Simplify log2(x3)−4log2(x)\log_2(x^3)-4\log_2(x)log2(x3)−4log2(x) into a single logarithm.
Simplify logb(a)+logb(b2)−2logb(a2)\log_b(a)+\log_b(b^2)-2\log_b(a^2)logb(a)+logb(b2)−2logb(a2) into a single logarithm.
Simplify 5logk(m)+logk(n)−2logk(p)5\log_k(m)+\log_k(n)-2\log_k(p)5logk(m)+logk(n)−2logk(p) into a single logarithm.
Simplify logx(y)−4logx(2y)\log_x(y)-4\log_x(2y)logx(y)−4logx(2y) into a single logarithm.
Simplify log3(x)+log3(2)−3log3(6)\log_3(x)+\log_3(2)-3\log_3(6)log3(x)+log3(2)−3log3(6) into a single logarithm.
Simplify 4log4(x)−2log4(x)4\log_4(\sqrt{x})-2\log_4(x)4log4(x)−2log4(x) into a single logarithm.
Simplify 2log2(x+1)−log2(4(x+1)2)2\log_2(x+1)-\log_2\bigl(4(x+1)^2\bigr)2log2(x+1)−log2(4(x+1)2) into a single logarithm.
Previous
Question Type 1: Using logarithm laws to solve numerical expressions
Next
Question Type 3: Using standard logarithms to rewrite expressions