Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.
Solve an exponential equation of the form a(b)^(ct)=d by isolating the exponential factor and taking logarithms
Problem
What is the solution to the exponential equation \(3\cdot~2^{4t}=48\)?
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What this problem is really about
Isolate the exponential expression before doing anything to the exponent. If the remaining constant can be rewritten with the same base, equate the exponents and solve the resulting linear equation; logarithms provide the general version of that move when bases do not match neatly. Finish by substituting into the original equation.
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