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

The answer to log_{2x^2}(x^3+1)=1 is x=1,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

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

The solution is x=1,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

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

x = 1, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

Decimal Notation

x = 1, x = 1.61803 \dots, x = - 0.61803 \dots

Solution steps

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

Apply log rules

\frac{ln ( x ^{3} + 1 )}{ln ( 2 x ^{2} )} = 1

Multiply both sides by

ln (2 x^{2})

\frac{ln ( x ^{3} + 1 )}{ln ( 2 x ^{2} )} ln (2 x^{2}) = 1 \cdot ln (2 x^{2})

Simplify

ln (x^{3} + 1) = ln (2 x^{2})

Apply log rules

x^{3} + 1 = 2 x^{2}

Solve

x^{3} + 1 = 2 x^{2} : x = 1, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

x = 1, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

Verify Solutions:

x = 1

True

, x = \frac{1 + 5}{2}

True

, x = \frac{1 - 5}{2}

True

The solutions are

x = 1, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

lo g_{3} (\frac{x + 1}{2 x + 1}) = 2

lo g_{10} (x) = 8

ln (x) = 10.12939661

x, 0.72 = ln (x)

lo g_{5} (x + 7) + lo g_{5} (x + 3) = 1

What is the answer to log_{2x^2}(x^3+1)=1 ?
The answer to log_{2x^2}(x^3+1)=1 is x=1,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2
Solve for x: log_{2x^2}(x^3+1)=1
The solution is x=1,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2