Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places.
\[
2^{t}=55
\]
There is no solution, \{\} .
The exact solution set is
\[
t \approx
\]
Answer
\(\boxed{t \approx 5.7814}\) is the final answer.
Step 1 ：The given equation is in the form of an exponential equation. To solve for t, we can take the logarithm of both sides. We can use either the common logarithm (base 10) or the natural logarithm (base e).
Step 2 ：The formula to convert from an exponential equation to a logarithmic equation is: If \(b^y = x\), then \(\log_b(x) = y\).
Step 3 ：So, we can rewrite the equation \(2^t = 55\) as \(\log_2(55) = t\).
Step 4 ：Using a calculator, we find that \(t = 5.78135971352466\).
Step 5 ：Rounding to four decimal places, we get \(t \approx 5.7814\).
Step 6 ：\(\boxed{t \approx 5.7814}\) is the final answer.
