Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.
Solve an exponential equation exactly and to four decimals
Problem
Solve \(2^x~=~9\) exactly with logarithms, round the solution to \(\text{four}~\text{decimal}~\text{places}\), and verify by substitution.
Big Picture
What this problem is really about
Taking logarithms turns the unknown exponent into a coefficient, leaving a linear equation whose solution is an exact logarithmic quotient. Keep that quotient intact for symbolic substitution, and use a separate calculator evaluation for the requested approximation. Rounding only at the end preserves both the exact check and the final decimal accuracy.
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