What is the answer to log_{2}(x)+4=5log_{x}(2) ?

The answer to log_{2}(x)+4=5log_{x}(2) is x=2,x= 1/32

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log_{2}(x)+4=5log_{x}(2)

lo g_{2} (x) + 4 = 5 lo g_{x} (2)

x = 2, x = \frac{1}{32}

Decimal Notation

x = 2, x = 0.03125

Solution steps

lo g_{2} (x) + 4 = 5 lo g_{x} (2)

Apply log rules

lo g_{2} (x) + 4 = \frac{5}{lo g _{2} ( x )}

Rewrite the equation with

lo g_{2} (x) = u

u + 4 = \frac{5}{u}

Solve

u + 4 = \frac{5}{u} : u = 1, u = - 5

u = 1, u = - 5

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 1 : x = 2

Solve

lo g_{2} (x) = - 5 : x = \frac{1}{32}

x = 2, x = \frac{1}{32}

Verify Solutions:

x = 2

True

, x = \frac{1}{32}

True

The solutions are

x = 2, x = \frac{1}{32}

ln (x) - ln (2 x + 1) = 1

y, ln (y) = ln (x)

7 = a lo g_{\frac{1}{3}} (4 x - 8) - 3

x ln (x) + x = 0

lo g_{8} (25) = 2 lo g_{8} (x)

What is the answer to log_{2}(x)+4=5log_{x}(2) ?
The answer to log_{2}(x)+4=5log_{x}(2) is x=2,x= 1/32
Solve for x: log_{2}(x)+4=5log_{x}(2)
The solution is x=2,x= 1/32