What is the answer to 2log_{x}(x+2)=3 ?

The answer to 2log_{x}(x+2)=3 is x\approx 2.87512…

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2log_{x}(x+2)=3

2 lo g_{x} (x + 2) = 3

x \approx 2.87512 \dots

Solution steps

2 lo g_{x} (x + 2) = 3

Divide both sides by

2

lo g_{x} (x + 2) = \frac{3}{2}

Apply log rules

\frac{ln ( x + 2 )}{ln ( x )} = \frac{3}{2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

ln (x + 2) \cdot 2 = ln (x) \cdot 3

Apply log rules

(x + 2)^{2} = x^{3}

Solve

(x + 2)^{2} = x^{3} : x \approx 2.87512 \dots

x \approx 2.87512 \dots

Verify Solutions:

x \approx 2.87512 \dots

True

The solution is

x \approx 2.87512 \dots

lo g_{2} (x) + 1 = lo g_{4} (x)

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

lo g_{4} (x + 10) = 2

lo g_{4} (x) = - 4

lo g_{4} (x) = - 8

What is the answer to 2log_{x}(x+2)=3 ?
The answer to 2log_{x}(x+2)=3 is x\approx 2.87512…
Solve for x: 2log_{x}(x+2)=3
The solution is x\approx 2.87512…