What is the answer to 4log_{5}(z)-log_{z}(5)=3 ?

The answer to 4log_{5}(z)-log_{z}(5)=3 is z=5,z= 1/(\sqrt[4]{5)}

Solve for z: 4log_{5}(z)-log_{z}(5)=3

The solution is z=5,z= 1/(\sqrt[4]{5)}

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4 lo g_{5} (z) - lo g_{z} (5) = 3

Decimal Notation

z = 5, z = 0.66874 \dots

Solution steps

4 lo g_{5} (z) - lo g_{z} (5) = 3

Apply log rules

4 lo g_{5} (z) - \frac{1}{lo g _{5} ( z )} = 3

Rewrite the equation with

lo g_{5} (z) = u

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

Solve

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

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

Substitute back

u = lo g_{5} (z),

solve for

z

Solve

lo g_{5} (z) = 1 : z = 5

Solve

Verify Solutions:

z = 5

True

The solutions are

lo g_{3} (12 x - 12) - lo g_{3} (x) = 2

lo g_{36} (x) = - \frac{1}{2}

lo g_{5} (x) = 7

lo g_{\frac{1}{3}} (x - 1) = - 2

ln (3 x - 2) = 2.8

What is the answer to 4log_{5}(z)-log_{z}(5)=3 ?
The answer to 4log_{5}(z)-log_{z}(5)=3 is z=5,z= 1/(\sqrt[4]{5)}
Solve for z: 4log_{5}(z)-log_{z}(5)=3
The solution is z=5,z= 1/(\sqrt[4]{5)}