Answer
$x=3-\sqrt[4]{1000}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\log(3-x)=0.75
,$ convert to exponential form. Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Since $\log x=\log_{10} x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} \log_{10}(3-x)=0.75 .\end{array}
Since $y=b^x$ is equivalent to $\log_b y=x,$ the exponential form of the equation above is \begin{array}{l}\require{cancel} 10^{0.75}=3-x .\end{array}
Using the properties of equality, the equation above is equivalent to \begin{array}{l}\require{cancel} x=3-10^{0.75}
\\\\
x=3-10^{\frac{3}{4}}
.\end{array}
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
x=3-\sqrt[4]{10^3}
\\\\
x=3-\sqrt[4]{1000}
.\end{array}
