What is the answer to solvefor x,yx=-log_{10}(x) ?

The answer to solvefor x,yx=-log_{10}(x) is x=(\W(ln(10)y))/(yln(10))

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solvefor x,yx=-log_{10}(x)

solve for

x, y x = - lo g_{10} (x)

x = \frac{W ( ln ( 10 ) y )}{y ln ( 10 )}

Solution steps

y x = - lo g_{10} (x)

Move

lo g_{10} (x)

to the left side

y x + lo g_{10} (x) = 0

Move

y x

to the right side

lo g_{10} (x) = - y x

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

1 0^{l o g_{10} (x)} = 1 0^{- y x}

Simplify

1 0^{l o g_{10} (x)} : x

x = 1 0^{- y x}

Solve

x = 1 0^{- y x} : x = \frac{W ( ln ( 10 ) y )}{y ln ( 10 )}

x = \frac{W ( ln ( 10 ) y )}{y ln ( 10 )}

Verify Solutions:

x = \frac{W ( ln ( 10 ) y )}{y ln ( 10 )}

True

The solution is

x = \frac{W ( ln ( 10 ) y )}{y ln ( 10 )}

0.78215 = 0.6446 ln (x) - 0.5557

- lo g_{10} (x) = 7

4 ln (4.6 x) = 7

4 lo g_{2} (3 - x) = 4

ln (3 x - 11) = 7

What is the answer to solvefor x,yx=-log_{10}(x) ?
The answer to solvefor x,yx=-log_{10}(x) is x=(\W(ln(10)y))/(yln(10))