What is the answer to ln(ax+b)-ln(cx+1)+e^3=5 ?

The answer to ln(ax+b)-ln(cx+1)+e^3=5 is x=(e^5-e^{e^3}b)/(e^{e^3)a-e^5c}

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

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}

Solution steps

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

Add

ln (c x + 1)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x, I n (lo g_{x} (3)) = 2

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

lo g_{x} (243) = - 5

What is the answer to ln(ax+b)-ln(cx+1)+e^3=5 ?
The answer to ln(ax+b)-ln(cx+1)+e^3=5 is x=(e^5-e^{e^3}b)/(e^{e^3)a-e^5c}