What is the answer to ln(6x)=ln(9)+2log_{10}(10) ?

The answer to ln(6x)=ln(9)+2log_{10}(10) is x=(3e^2)/2

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ln(6x)=ln(9)+2log_{10}(10)

ln (6 x) = ln (9) + 2 lo g_{10} (10)

x = \frac{3 e ^{2}}{2}

Decimal Notation

x = 11.08358 \dots

Solution steps

ln (6 x) = ln (9) + 2 lo g_{10} (10)

Apply log rules

6 x = 9 e^{2}

Solve

6 x = 9 e^{2} : x = \frac{3 e ^{2}}{2}

x = \frac{3 e ^{2}}{2}

5 lo g_{10} (u) = 0

lo g_{3} (y) - 4 = lo g_{3} (5)

lo g_{10} (x + 10) = - 1

2 ln (4 x) = 2 + ln (9)

lo g_{10} (5) + lo g_{10} (x) = 1

What is the answer to ln(6x)=ln(9)+2log_{10}(10) ?
The answer to ln(6x)=ln(9)+2log_{10}(10) is x=(3e^2)/2
Solve for x: ln(6x)=ln(9)+2log_{10}(10)
The solution is x=(3e^2)/2