What is the answer to log_{5}(x)-2log_{x}(5)=3 ?

The answer to log_{5}(x)-2log_{x}(5)=3 is x=5^{(3+sqrt(17))/2},x=5^{(3-sqrt(17))/2}

Solve for x: log_{5}(x)-2log_{x}(5)=3

The solution is x=5^{(3+sqrt(17))/2},x=5^{(3-sqrt(17))/2}

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lo g_{5} (x) - 2 lo g_{x} (5) = 3

x = 5^{\frac{3 + 17}{2}}, x = 5^{\frac{3 - 17}{2}}

Decimal Notation

x = 308.61610 \dots, x = 0.40503 \dots

Solution steps

lo g_{5} (x) - 2 lo g_{x} (5) = 3

Apply log rules

lo g_{5} (x) - \frac{2}{lo g _{5} ( x )} = 3

Rewrite the equation with

lo g_{5} (x) = u

u - \frac{2}{u} = 3

Solve

u - \frac{2}{u} = 3 : u = \frac{3 + 17}{2}, u = \frac{3 - 17}{2}

u = \frac{3 + 17}{2}, u = \frac{3 - 17}{2}

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = \frac{3 + 17}{2} : x = 5^{\frac{3 + 17}{2}}

Solve

lo g_{5} (x) = \frac{3 - 17}{2} : x = 5^{\frac{3 - 17}{2}}

x = 5^{\frac{3 + 17}{2}}, x = 5^{\frac{3 - 17}{2}}

Verify Solutions:

x = 5^{\frac{3 + 17}{2}}

True

, x = 5^{\frac{3 - 17}{2}}

True

The solutions are

x = 5^{\frac{3 + 17}{2}}, x = 5^{\frac{3 - 17}{2}}

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

lo g_{x} (0.001) = - 3

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

x, z = ln (x y)

lo g_{10} (x) = 4.9

What is the answer to log_{5}(x)-2log_{x}(5)=3 ?
The answer to log_{5}(x)-2log_{x}(5)=3 is x=5^{(3+sqrt(17))/2},x=5^{(3-sqrt(17))/2}
Solve for x: log_{5}(x)-2log_{x}(5)=3
The solution is x=5^{(3+sqrt(17))/2},x=5^{(3-sqrt(17))/2}