Solve log_a(x)=b and evaluate logarithmic functions
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Solve log_a(x) = b for x
log_(x) =
Evaluate log_a(x)
log_()
Result
Derivation
Logarithmic Function Properties
log_a(x) = b means x = a^b
Domain: x>0, base a>0, a!=1
log(ab)=log(a)+log(b), log(a^n)=n*log(a)
Change of base: log_a(b) = ln(b)/ln(a)
Logarithms are the inverse of exponentials. To solve log_a(x)=b, convert to exponential form: x = a^b. The argument of a log must always be positive. Use log properties to combine or expand log expressions before solving.
⚠The argument of a logarithm must be positive. Always check your solution by plugging back into the original equation.
What Are Logarithmic Functions?
The logarithm log_a(x) answers: what exponent makes a equal x? f(x)=log_a(x) is the inverse of f(x)=a^x. Domain (0,inf), range (-inf,inf). Natural log ln(x) uses base e. Common log log(x) uses base 10.
Definition
log_a(x) = y means a^y = x. Inverse of exponential. Domain x>0. Range all reals. Asymptote at x=0.
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