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Popular >

2log_{10}(x-2)=2x-7

Solution

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

Solution

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - 2 ln ( 10 )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - 2 ln ( 10 )}{ln ( 10 )}

+1

Decimal Notation

x = 3.74073 \dots, x = 2.03421 \dots

Solution steps

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

Divide both sides by

2

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

If

f (x) = g (x),

then

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

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

Simplify

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

x - 2 = 1 0^{\frac{2 x - 7}{2}}

Solve

x - 2 = 1 0^{\frac{2 x - 7}{2}} : x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - 2 ln ( 10 )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - 2 ln ( 10 )}{ln ( 10 )}

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - 2 ln ( 10 )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - 2 ln ( 10 )}{ln ( 10 )}

Verify Solutions:

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - 2 ln ( 10 )}{ln ( 10 )}

True

, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - 2 ln ( 10 )}{ln ( 10 )}

True

The solutions are

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - 2 ln ( 10 )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - 2 ln ( 10 )}{ln ( 10 )}

Popular Examples

log_{x}(64)+3*log_{4}(x)-log_{x}(4)=5

lo g_{x} (64) + 3 \cdot lo g_{4} (x) - lo g_{x} (4) = 5

lo g_{27} (x) = 3

1/(2log_{10)(7x-3)}=-5

\frac{1}{2 lo g _{10} ( 7 x - 3 )} = - 5

solvefor x,ln(y-x^2)=k solve for

x, ln (y - x^{2}) = k

log_{5}(x^3)+13x-5=0

lo g_{5} (x^{3}) + 13 x - 5 = 0

Frequently Asked Questions (FAQ)

What is the answer to 2log_{10}(x-2)=2x-7 ?
The answer to 2log_{10}(x-2)=2x-7 is
Solve for x: 2log_{10}(x-2)=2x-7
The solution is