What is the answer to 3log_{3}(x)+4log_{x}(3)=7 ?

The answer to 3log_{3}(x)+4log_{x}(3)=7 is x=3\sqrt[3]{3},x=3

Solve for x: 3log_{3}(x)+4log_{x}(3)=7

The solution is x=3\sqrt[3]{3},x=3

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

Decimal Notation

x = 4.32674 \dots, x = 3

Solution steps

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

Apply log rules

3 lo g_{3} (x) + \frac{4}{lo g _{3} ( x )} = 7

Rewrite the equation with

lo g_{3} (x) = u

3 u + \frac{4}{u} = 7

Solve

3 u + \frac{4}{u} = 7 : u = \frac{4}{3}, u = 1

u = \frac{4}{3}, u = 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = 1 : x = 3

Verify Solutions:

True

, x = 3

True

The solutions are

x, ln (x) + ln (y) + x y = 3

x, ln (x^{2}) = 18

ln (t) = 0.96 ln (16) + 0.2

x, ln (x^{2}) = 20

lo g_{9} (x) = \frac{- 3}{2}

What is the answer to 3log_{3}(x)+4log_{x}(3)=7 ?
The answer to 3log_{3}(x)+4log_{x}(3)=7 is x=3\sqrt[3]{3},x=3
Solve for x: 3log_{3}(x)+4log_{x}(3)=7
The solution is x=3\sqrt[3]{3},x=3