What is the answer to ln(7)=ln(q^2)+5-ln(10) ?

The answer to ln(7)=ln(q^2)+5-ln(10) is q=sqrt((70)/(e^5)),q=-sqrt((70)/(e^5))

Solve for q: ln(7)=ln(q^2)+5-ln(10)

The solution is q=sqrt((70)/(e^5)),q=-sqrt((70)/(e^5))

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ln (7) = ln (q^{2}) + 5 - ln (10)

q = \frac{70}{e ^{5}}, q = - \frac{70}{e ^{5}}

Decimal Notation

q = 0.68677 \dots, q = - 0.68677 \dots

Solution steps

ln (7) = ln (q^{2}) + 5 - ln (10)

Switch sides

ln (q^{2}) + 5 - ln (10) = ln (7)

Move

ln (10)

to the right side

ln (q^{2}) + 5 = ln (7) + ln (10)

Move

5

to the right side

ln (q^{2}) = ln (7) + ln (10) - 5

Apply log rules

q^{2} = \frac{70}{e ^{5}}

Solve

q^{2} = \frac{70}{e ^{5}} : q = \frac{70}{e ^{5}}, q = - \frac{70}{e ^{5}}

q = \frac{70}{e ^{5}}, q = - \frac{70}{e ^{5}}

Verify Solutions:

q = \frac{70}{e ^{5}}

True

, q = - \frac{70}{e ^{5}}

True

The solutions are

q = \frac{70}{e ^{5}}, q = - \frac{70}{e ^{5}}

lo g_{10} (x) = 130

x, ln (y) = x + ln (x - 5) + c

lo g_{5} (1 lo g_{3} (x)) = 0

ln (x) = ln (x - 1) + 1

2 lo g_{3} (6) - 2 lo g_{3} (x) = 9

What is the answer to ln(7)=ln(q^2)+5-ln(10) ?
The answer to ln(7)=ln(q^2)+5-ln(10) is q=sqrt((70)/(e^5)),q=-sqrt((70)/(e^5))
Solve for q: ln(7)=ln(q^2)+5-ln(10)
The solution is q=sqrt((70)/(e^5)),q=-sqrt((70)/(e^5))