What is the answer to x^2+9^{log_{3}(x)}=30 ?

The answer to x^2+9^{log_{3}(x)}=30 is x=sqrt(15)

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x^2+9^{log_{3}(x)}=30

x^{2} + 9^{l o g_{3} (x)} = 30

x = 15

Decimal

x = 3.87298 \dots

Solution steps

x^{2} + 9^{l o g_{3} (x)} = 30

Move

x^{2}

to the right side

9^{l o g_{3} (x)} = 30 - x^{2}

Apply log rules

x^{2} = 30 - x^{2}

Solve

x^{2} = 30 - x^{2} : x = 15, x = - 15

x = 15, x = - 15

Verify Solutions:

x = 15

True

, x = - 15

False

The solution is

x = 15

3 ln (2 x - 7) = 9

ln (x) = 10

ln (x) + ln (2 x + 1) = 2

lo g_{6} (x^{2} - 5 x) = 2

- 7 + lo g_{3} (4 - x) = - 6

What is the answer to x^2+9^{log_{3}(x)}=30 ?
The answer to x^2+9^{log_{3}(x)}=30 is x=sqrt(15)
Solve for x: x^2+9^{log_{3}(x)}=30
The solution is x=sqrt(15)