Solve the equation $2(4^x)-8=11(2^x)-2^{2x+3}$, giving your answer correct to $3$ significant fi

Question

Solve the equation $2(4^x)-8=11(2^x)-2^{2x+3}$, giving your answer correct to $3$ significant figures.[5] Show that the solution from part (a) may be written in the form $m-\log_np$ where $m$, $n$, and $p$ are integers to be determined.[2]

Accepted Answer

(a) $x=0.678$ $\text{(3 s.f.)}$ (b) $x=3-\log_2 5$, where $m=3$, $n=2$, $p=5$.

Exponential and Logarithmic Functions - Conversion between Exponential and Logarithm Form

Exponential and Logarithmic Functions - Conversion between Exponential and Logarithm Form

Solution:

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