Evaluate logarithmic expressions
Evaluate log_b(x) exactly, including negative and fractional exponent cases. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Evaluate the logarithm exactly.
log3(9)
Answer: 2
See one solved, step by step
Evaluate the logarithm exactly.
log5(125)
📘 Worked solution
1Let L = log5(125).Give the unknown log value a name so we can solve for it.
25L = 125By definition, log_b(x) = L means b^L = x.
3(51)L = 53 [since 5 = 51 and 125 = 53]Rewrite both sides as a power of the same number, 5.
451L = 53A power raised to a power multiplies the exponents.
51L = 3 => L = 3Same base on both sides means the exponents must be equal — divide to solve for L.
Ready to master it?
Jump into unlimited practice — your Winny Score tracks you to 100. And if it won't click, a real tutor will make it click: first lesson free.
Start practicing