What is the answer to 2+log_{2}(x)=15log_{x}(2) ?

The answer to 2+log_{2}(x)=15log_{x}(2) is x=8,x= 1/32

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2+log_{2}(x)=15log_{x}(2)

2 + lo g_{2} (x) = 15 lo g_{x} (2)

x = 8, x = \frac{1}{32}

Decimal Notation

x = 8, x = 0.03125

Solution steps

2 + lo g_{2} (x) = 15 lo g_{x} (2)

Apply log rules

2 + lo g_{2} (x) = \frac{15}{lo g _{2} ( x )}

Rewrite the equation with

lo g_{2} (x) = u

2 + u = \frac{15}{u}

Solve

2 + u = \frac{15}{u} : u = 3, u = - 5

u = 3, u = - 5

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 3 : x = 8

Solve

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

x = 8, x = \frac{1}{32}

Verify Solutions:

x = 8

True

, x = \frac{1}{32}

True

The solutions are

x = 8, x = \frac{1}{32}

ln (\frac{10}{7 - 2 x}) = ln (2 x)

lo g_{4} (x) = - 3

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

e^{l n (x)} = x

ln (x + 31) - ln (4 - 3 x) = 5 ln (2)

What is the answer to 2+log_{2}(x)=15log_{x}(2) ?
The answer to 2+log_{2}(x)=15log_{x}(2) is x=8,x= 1/32
Solve for x: 2+log_{2}(x)=15log_{x}(2)
The solution is x=8,x= 1/32