Question

Solve 10^×=3I see that the answer is 0.477 but i would like to know step by step on how they got the answer. i dont understand how the term "take the log of both sides"

Answer 1

x=0.4771

Explanation:

Given the equation:

`10^x=3`

Whenever the unknown is in the exponent, it is best to take the logarithm of both sides of the equation.

`\log10^x=\log3`

Next, apply the power law of logarithms to the left-hand side of the equation above:

`\begin{gathered} \log a^n=n\log a \\ \implies\log10^x=x\log10 \end{gathered}`

Thus, the last result can be written in the form below:

`\begin{gathered} x\log10=\log3 \\ \text{ The log of 10 is 1} \\ x*1=\log3 \\ x=0.4771 \end{gathered}`

The value of x is approximately 0.4771.