Solve the equation:

\[
\log(6x - 3) = -4
\]

0\to x > 0\to x\in\mathbb{R^+}\\\\log6x=-4+3\\\\log6x=-1\iff10^{-1}=6x\\\\6x=\frac{1}{10}\ \ \ /:6\\\\x=\frac{1}{60}\in D"> l o g 6 x − 3 = − 4 ; D : 6 x > 0 → x > 0 → x ∈ R + l o g 6 x = − 4 + 3 l o g 6 x = − 1 ⟺ 1 0 − 1 = 6 x 6 x = 10 1 ​ / : 6 x = 60 1 ​ ∈ D

Answered by Anonymous | 2024-06-10

To solve lo g ( 6 x − 3 ) = − 4 , we rewrite it in exponential form as 6 x − 3 = 0.0001 . By isolating x , we find that x ≈ 0.50001667 , which meets the necessary conditions for logarithms. Therefore, the solution to the equation is approximately x ≈ 0.50001667 .
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Answered by Anonymous | 2024-12-20