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Popular >

log_{10}(2x+1)=3x-2

Solution

lo g_{10} (2 x + 1) = 3 x - 2

Solution

x = - \frac{2 W _{- 1} ( - \frac{3 l n ( 10 )}{200 e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{6 ln ( 10 )}, x = - \frac{2 W _{0} ( - \frac{3 l n ( 10 )}{200 e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{6 ln ( 10 )}

+1

Decimal Notation

x = 0.80561 \dots, x = - 0.49984 \dots

Solution steps

lo g_{10} (2 x + 1) = 3 x - 2

If

f (x) = g (x),

then

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

1 0^{l o g_{10} (2 x + 1)} = 1 0^{3 x - 2}

Simplify

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

2 x + 1 = 1 0^{3 x - 2}

Solve

2 x + 1 = 1 0^{3 x - 2} : x = - \frac{2 W _{- 1} ( - \frac{3 l n ( 10 )}{200 e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{6 ln ( 10 )}, x = - \frac{2 W _{0} ( - \frac{3 l n ( 10 )}{200 e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{6 ln ( 10 )}

x = - \frac{2 W _{- 1} ( - \frac{3 l n ( 10 )}{200 e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{6 ln ( 10 )}, x = - \frac{2 W _{0} ( - \frac{3 l n ( 10 )}{200 e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{6 ln ( 10 )}

Verify Solutions:

x = - \frac{2 W _{- 1} ( - \frac{3 l n ( 10 )}{200 e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{6 ln ( 10 )}

True

, x = - \frac{2 W _{0} ( - \frac{3 l n ( 10 )}{200 e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{6 ln ( 10 )}

True

The solutions are

x = - \frac{2 W _{- 1} ( - \frac{3 l n ( 10 )}{200 e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{6 ln ( 10 )}, x = - \frac{2 W _{0} ( - \frac{3 l n ( 10 )}{200 e ^{\frac{3 l n ( 10 )}{2}}} ) + 3 ln ( 10 )}{6 ln ( 10 )}

Popular Examples

lo g_{9} (x) = - 3

log_{2}(x^2+2)=3

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

log_{4}(x-4)=1-log_{4}(x-7)

lo g_{4} (x - 4) = 1 - lo g_{4} (x - 7)

log_{6}(8x)-3log_{6}(3)=2

lo g_{6} (8 x) - 3 lo g_{6} (3) = 2

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

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

Frequently Asked Questions (FAQ)

What is the answer to log_{10}(2x+1)=3x-2 ?
The answer to log_{10}(2x+1)=3x-2 is
Solve for x: log_{10}(2x+1)=3x-2
The solution is