Logaritmi

Formule de calcul in rezolvarea exercitiilor cu logaritmi

Conditii de existenta pentru logaritmi

  log_{{a}}x \qquad :          x\qquad >\qquad 0 \\<br />
a \qquad > \qquad 0 \\<br />
a \qquad \neq \qquad 1

Notatii logaritmi

log _ {e} \to ln

log _ {a}1 \qquad = \qquad 1

 

log _ {a}A ^{n} \qquad = n\cdot log_ {a}A

a ^ {log_{a}^\qquad {A}} = \quad A

Adunarea si scaderea logaritmilor

log _ {a}A \qquad + log_{a}B = log _ {a} (A\cdot B)

log _ {a}A \qquad - log_{a}B = log _ {a} \qquad \frac{A}{B}

log _ {a}A ^{n} \qquad = n\cdot log_ {a}A

a ^ {log_{a}^\qquad {A}} = \quad A

Ecuatii logaritmice

1.
log _ {a} (expresie)=b
expresie = a^{b}

Conditie expr \qquad > \qquad 0

2.
log _ {a} (expr1) \qquad = \qquad log_{a}(expr2)
expr1 \qquad = \qquad expr2

Conditie

expr1 \qquad > \qquad 0

expr2 \qquad > \qquad 0

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