Question

solve for x. you may round your answer to 3 decimal places.
10^{x + 3} - 51 = 389

Explanation:

Step1: Isolate the exponential term

Add 51 to both sides of the equation \(10^{x + 3}-51 = 389\) to get \(10^{x+3}=389 + 51\).
\(10^{x+3}=440\)

Step2: Take the logarithm of both sides

Take the common logarithm (base 10) of both sides. Since \(\log_{10}(10^{a})=a\), we have \(\log_{10}(10^{x + 3})=\log_{10}(440)\), which simplifies to \(x + 3=\log_{10}(440)\).

Step3: Solve for x

Subtract 3 from both sides: \(x=\log_{10}(440)-3\).
Calculate \(\log_{10}(440)\approx2.643452676\), then \(x\approx2.643452676 - 3=- 0.356547324\approx - 0.357\) (rounded to 3 decimal places).

Answer:

\(x\approx - 0.357\)