What is the answer to (log_{3}(x+8)+1)/(2*log_{3)(x^2)}=2 ?

The answer to (log_{3}(x+8)+1)/(2*log_{3)(x^2)}=2 is x\approx-1.45098…,x\approx 1.52045…

Solve for x: (log_{3}(x+8)+1)/(2*log_{3)(x^2)}=2

The solution is x\approx-1.45098…,x\approx 1.52045…

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\frac{lo g _{3} ( x + 8 ) + 1}{2 \cdot lo g _{3} ( x ^{2} )} = 2

x \approx - 1.45098 \dots, x \approx 1.52045 \dots

Solution steps

\frac{lo g _{3} ( x + 8 ) + 1}{2 lo g _{3} ( x ^{2} )} = 2

Multiply both sides by

2 lo g_{3} (x^{2})

\frac{lo g _{3} ( x + 8 ) + 1}{2 lo g _{3} ( x ^{2} )} \cdot 2 lo g_{3} (x^{2}) = 2 \cdot 2 lo g_{3} (x^{2})

Simplify

lo g_{3} (x + 8) + 1 = 4 lo g_{3} (x^{2})

Apply log rules

(x + 8) \cdot 3 = x^{8}

Solve

(x + 8) \cdot 3 = x^{8} : x \approx - 1.45098 \dots, x \approx 1.52045 \dots

x \approx - 1.45098 \dots, x \approx 1.52045 \dots

Verify Solutions:

x \approx - 1.45098 \dots

True

, x \approx 1.52045 \dots

True

The solutions are

x \approx - 1.45098 \dots, x \approx 1.52045 \dots

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

\frac{( lo g _{10} ( x ) )}{( lo g _{10} ( x ) + 1 )} = - 1

lo g_{5} ((2 x + 3)^{2}) - lo g_{5} (x) = 2

lo g_{3} (lo g_{5} (x - 2)) = - 1

lo g_{10} (x) = 1 - lo g_{10} (x - 3)

What is the answer to (log_{3}(x+8)+1)/(2*log_{3)(x^2)}=2 ?
The answer to (log_{3}(x+8)+1)/(2*log_{3)(x^2)}=2 is x\approx-1.45098…,x\approx 1.52045…
Solve for x: (log_{3}(x+8)+1)/(2*log_{3)(x^2)}=2
The solution is x\approx-1.45098…,x\approx 1.52045…