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

The answer to log_{x}(3)=log_{3}(9x)^3 is x=1.12463…,x=0.05056…

Solve for x: log_{x}(3)=log_{3}(9x)^3

The solution is x=1.12463…,x=0.05056…

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lo g_{x} (3) = lo g_{3} (9 x)^{3}

x = 1.12463 \dots, x = 0.05056 \dots

Solution steps

lo g_{x} (3) = lo g_{3} (9 x)^{3}

Apply log rules

\frac{1}{lo g _{3} ( x )} = (lo g_{3} (9) + lo g_{3} (x))^{3}

Rewrite the equation with

lo g_{3} (x) = u

\frac{1}{u} = (lo g_{3} (9) + u)^{3}

Solve

\frac{1}{u} = (lo g_{3} (9) + u)^{3} : u \approx 0.10691 \dots, u \approx - 2.71667 \dots

u \approx 0.10691 \dots, u \approx - 2.71667 \dots

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = 0.10691 \dots : x = 1.12463 \dots

Solve

lo g_{3} (x) = - 2.71667 \dots : x = 0.05056 \dots

x = 1.12463 \dots, x = 0.05056 \dots

Verify Solutions:

x = 1.12463 \dots

True

, x = 0.05056 \dots

True

The solutions are

x = 1.12463 \dots, x = 0.05056 \dots

\frac{1}{e ^{0.243}} = ln (x)

lo g_{10} (P) = 4.4366

8 - 2 ln (x) = 7

lo g_{a} (2 x - 3) = b

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

What is the answer to log_{x}(3)=log_{3}(9x)^3 ?
The answer to log_{x}(3)=log_{3}(9x)^3 is x=1.12463…,x=0.05056…
Solve for x: log_{x}(3)=log_{3}(9x)^3
The solution is x=1.12463…,x=0.05056…