ln(ax+b)-ln(cx+1)+e^3=5

Lösung

ln (a x + b) - ln (c x + 1) + e^{3} = 5

x = \frac{e ^{5} - e ^{e^{3}} b}{e ^{e^{3}} a - e ^{5} c}

Schritte zur Lösung

ln (a x + b) - ln (c x + 1) + e^{3} = 5

Füge

ln (c x + 1)

zu beiden Seiten hinzu

ln (a x + b) - ln (c x + 1) + e^{3} + ln (c x + 1) = 5 + ln (c x + 1)

Vereinfache

e^{3} + ln (a x + b) = 5 + ln (c x + 1)

Wende die log Regel an

e^{e^{3}} (a x + b) = e^{5} (c x + 1)

Löse

e^{e^{3}} (a x + b) = e^{5} (c x + 1) : x = \frac{e ^{5} - e ^{e^{3}} b}{e ^{e^{3}} a - e ^{5} c}

x = \frac{e ^{5} - e ^{e^{3}} b}{e ^{e^{3}} a - e ^{5} c}

(lo g_{2} (x)) = 0

lo g_{2} (2 x + 1) - lo g_{2} (x + 3) = 0

so l v e f or x, I n (lo g_{x} (3)) = 2

\frac{lo g _{4} ( 15 x + 1 ) 1}{2} = 2

lo g_{x} (243) = - 5