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Logarithmic Function Calculator

Online logarithmic function calculator: enter the base a and argument x to evaluate y=log_a x. It is the inverse of the exponential, grows slowly, and suits wide-ranging data (decibels, magnitude, pH).

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y=log_a x (a>0,a≠1,x>0)
(1,0)
a>0,a≠1
x>0

📖 Tutorial | Logarithmic Function

1. Definition
The function y=log_a x (a>0,a≠1,x>0) is the logarithmic function, the inverse of y=a^x.
2. Formula & Notation
aBase (a>0,a≠1)
xArgument (x>0)
yAny real number
3. Properties & Laws
  • Domain (0,+∞), range R;
  • Passes through (1,0);
  • Increases for a>1, decreases for 0<a<1;
  • The y-axis (x=0) is the vertical asymptote;
  • Symmetric to y=a^x across y=x.
4. Steps
  1. Enter the base a and argument x;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: Since 2³=8, log₂8=3.
6. Common Pitfalls
x must be positive;
The graph lies right of the y-axis;
Domain and range swap with the exponential.

❓ FAQ | Logarithmic Function

Definition?
y=log_a x (a>0,a≠1,x>0).
Domain, range?
(0,+∞) and R.
Point?
(1,0).
Monotonicity?
a>1 increases.
Asymptote?
The y-axis x=0.
With exponential?
Inverse, symmetric about y=x.
Slow growth?
Suits wide-ranging data.