Answer:
x=0.4771
Explanation:
Given the equation:
[tex]10^x=3[/tex]Whenever the unknown is in the exponent, it is best to take the logarithm of both sides of the equation.
[tex]\log10^x=\log3[/tex]Next, apply the power law of logarithms to the left-hand side of the equation above:
[tex]\begin{gathered} \log a^n=n\log a \\ \implies\log10^x=x\log10 \end{gathered}[/tex]Thus, the last result can be written in the form below:
[tex]\begin{gathered} x\log10=\log3 \\ \text{ The log of 10 is 1} \\ x\times1=\log3 \\ x=0.4771 \end{gathered}[/tex]The value of x is approximately 0.4771.
