What is the answer to solvefor p,log_{10}(p(x)^2)+log_{10}(p)(x-1)=0 ?

The answer to solvefor p,log_{10}(p(x)^2)+log_{10}(p)(x-1)=0 is p=10^{-(2log_{10}(x))/x}

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solvefor p,log_{10}(p(x)^2)+log_{10}(p)(x-1)=0

solve for

p, lo g_{10} (p (x)^{2}) + lo g_{10} (p) (x - 1) = 0

p = 1 0^{- \frac{2 l o g _{10} ( x )}{x}}

Solution steps

lo g_{10} (p x^{2}) + lo g_{10} (p) (x - 1) = 0

Apply log rules

p = 1 0^{- \frac{l o g _{10} ( x ^{2} )}{x}}

Solve

p = 1 0^{- \frac{l o g _{10} ( x ^{2} )}{x}} : p = 1 0^{- \frac{2 l o g _{10} ( x )}{x}}

p = 1 0^{- \frac{2 l o g _{10} ( x )}{x}}

Verify Solutions:

p = 1 0^{- \frac{2 l o g _{10} ( x )}{x}}

True

The solution is

p = 1 0^{- \frac{2 l o g _{10} ( x )}{x}}

\frac{lo g _{3} ( x + 8 ) + 1}{2 \cdot lo g _{3} ( x ^{2} )} = 2

ln (x) = \frac{2}{3}

\frac{( lo g _{10} ( x ) )}{( lo g _{10} ( x ) + 1 )} = - 1

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

lo g_{3} (lo g_{5} (x - 2)) = - 1

What is the answer to solvefor p,log_{10}(p(x)^2)+log_{10}(p)(x-1)=0 ?
The answer to solvefor p,log_{10}(p(x)^2)+log_{10}(p)(x-1)=0 is p=10^{-(2log_{10}(x))/x}