What is the answer to x=(log_{10}(x)+7)/2 ?

The answer to x=(log_{10}(x)+7)/2 is x=-(\W_{0}(-\frac{ln(10))/(5000000))}{2ln(10)}

Solve for x: x=(log_{10}(x)+7)/2

The solution is x=-(\W_{0}(-\frac{ln(10))/(5000000))}{2ln(10)}

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x = \frac{lo g _{10} ( x ) + 7}{2}

x = - \frac{W _{0} ( - \frac{l n ( 10 )}{5000000} )}{2 ln ( 10 )}

Decimal Notation

x = 0.0000001

Solution steps

x = \frac{lo g _{10} ( x ) + 7}{2}

Switch sides

\frac{lo g _{10} ( x ) + 7}{2} = x

Multiply both sides by

2

lo g_{10} (x) + 7 = 2 x

Move

7

to the right side

lo g_{10} (x) = 2 x - 7

f (x) = g (x),

then

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

1 0^{l o g_{10} (x)} = 1 0^{2 x - 7}

Simplify

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

x = 1 0^{2 x - 7}

Solve

x = 1 0^{2 x - 7} : x = - \frac{W _{0} ( - \frac{l n ( 10 )}{5000000} )}{2 ln ( 10 )}

x = - \frac{W _{0} ( - \frac{l n ( 10 )}{5000000} )}{2 ln ( 10 )}

Verify Solutions:

x = - \frac{W _{0} ( - \frac{l n ( 10 )}{5000000} )}{2 ln ( 10 )}

True

The solution is

x = - \frac{W _{0} ( - \frac{l n ( 10 )}{5000000} )}{2 ln ( 10 )}

lo g_{a} (1) = 0

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

1 + lo g_{10} (x) = lo g_{10} (x + 1)

ln (x - 2) + ln (x + 2) = ln (3 x)

lo g_{9} (x + 1) - lo g_{9} (1 - x) = lo g_{9} (2 x + 3)

What is the answer to x=(log_{10}(x)+7)/2 ?
The answer to x=(log_{10}(x)+7)/2 is x=-(\W_{0}(-\frac{ln(10))/(5000000))}{2ln(10)}
Solve for x: x=(log_{10}(x)+7)/2
The solution is x=-(\W_{0}(-\frac{ln(10))/(5000000))}{2ln(10)}