What is the answer to log_{2}(x)=4-log_{x}(2) ?

The answer to log_{2}(x)=4-log_{x}(2) is x=2^{2+sqrt(3)},x=2^{2-sqrt(3)}

Solve for x: log_{2}(x)=4-log_{x}(2)

The solution is x=2^{2+sqrt(3)},x=2^{2-sqrt(3)}

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lo g_{2} (x) = 4 - lo g_{x} (2)

x = 2^{2 + 3}, x = 2^{2 - 3}

Decimal Notation

x = 13.28798 \dots, x = 1.20409 \dots

Solution steps

lo g_{2} (x) = 4 - lo g_{x} (2)

Apply log rules

lo g_{2} (x) = 4 - \frac{1}{lo g _{2} ( x )}

Rewrite the equation with

lo g_{2} (x) = u

u = 4 - \frac{1}{u}

Solve

u = 4 - \frac{1}{u} : u = 2 + 3, u = 2 - 3

u = 2 + 3, u = 2 - 3

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

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

Solve

lo g_{2} (x) = 2 - 3 : x = 2^{2 - 3}

x = 2^{2 + 3}, x = 2^{2 - 3}

Verify Solutions:

x = 2^{2 + 3}

True

, x = 2^{2 - 3}

True

The solutions are

x = 2^{2 + 3}, x = 2^{2 - 3}

2 ln (x - 2) + ln (x + 8) = 3 ln (x)

lo g_{5} (y) = - 3

ln (x) = ln (x - 2000) + 14876

- 4 ln (5 x + 2) = 11

lo g_{5} (x + 15) - lo g_{5} (x - 9) = 2

What is the answer to log_{2}(x)=4-log_{x}(2) ?
The answer to log_{2}(x)=4-log_{x}(2) is x=2^{2+sqrt(3)},x=2^{2-sqrt(3)}
Solve for x: log_{2}(x)=4-log_{x}(2)
The solution is x=2^{2+sqrt(3)},x=2^{2-sqrt(3)}