What is the answer to log_{x+5}(2x^2+1)=2 ?

The answer to log_{x+5}(2x^2+1)=2 is x=-2,x=12

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log_{x+5}(2x^2+1)=2

lo g_{x + 5} (2 x^{2} + 1) = 2

x = - 2, x = 12

Solution steps

lo g_{x + 5} (2 x^{2} + 1) = 2

Apply log rules

\frac{ln ( 2 x ^{2} + 1 )}{ln ( x + 5 )} = 2

Multiply both sides by

ln (x + 5)

\frac{ln ( 2 x ^{2} + 1 )}{ln ( x + 5 )} ln (x + 5) = 2 ln (x + 5)

Simplify

ln (2 x^{2} + 1) = 2 ln (x + 5)

Apply log rules

2 x^{2} + 1 = (x + 5)^{2}

Solve

2 x^{2} + 1 = (x + 5)^{2} : x = - 2, x = 12

x = - 2, x = 12

Verify Solutions:

x = - 2

True

, x = 12

True

The solutions are

x = - 2, x = 12

3.28 = 11.6 \cdot ln (c)

10 lo g_{7} (x - 3) = 66

ln (x^{3}) = 7

lo g_{c} (c^{6}) = 6

3 lo g_{3} (x) = 5

What is the answer to log_{x+5}(2x^2+1)=2 ?
The answer to log_{x+5}(2x^2+1)=2 is x=-2,x=12
Solve for x: log_{x+5}(2x^2+1)=2
The solution is x=-2,x=12