Given that $$\(\frac{2^{3 x+2}+8}{2^{3 x}-7}=5\)$$, find the value of $$\(2^{3 x}\)$$ and hence, using logarithms, find the value of $$\(x\)$$ correct to 4 significant figures. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_w20_qp_22 Year：2020 Question No：2
Answer:
Use \(2^{3 x+2}=4 \times 2^{3 x}\)
Solve equation for \(2^{3 x}\)
Obtain \(2^{3 x}=43\)
Apply logarithms and use power law for \(2^{3 x}=k\) where \(k>0\)
Obtain \(1.809\)
Solve equation for \(2^{3 x}\)
Obtain \(2^{3 x}=43\)
Apply logarithms and use power law for \(2^{3 x}=k\) where \(k>0\)
Obtain \(1.809\)
Knowledge points:
2.2.3 use logarithms to solve equations and inequalities in which the unknown appears in indices
Solution:
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