Find the value of $$\(x\)$$ for which $$\(3\left(2^{1-x}\right)=7^{x}\)$$. Give your answer in the form $$\(\frac{\ln a}{\ln b}\)$$, where $$\(a\)$$ and $$\(b\)$$ are integers. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_w21_qp_32 Year：2021 Question No：1
Answer:
Use law of the logarithm of a product, a quotient or power
Obtain a correct linear equation in any form
Solve a linear equation for \(x\)
Obtain answer \(x=\frac{\ln 6}{\ln 14}\)
Alternative method for Question 1
\(\begin{array}{l}
2^{1-x}=2 \times 2^{-x}
6=2^{x} 7^{x}\left[=14^{x}\right]
\end{array}\)
Use law of the logarithm of a power to solve for \(x\)
Obtain answer \(x=\frac{\ln 6}{\ln 14}\)
Obtain a correct linear equation in any form
Solve a linear equation for \(x\)
Obtain answer \(x=\frac{\ln 6}{\ln 14}\)
Alternative method for Question 1
\(\begin{array}{l}
2^{1-x}=2 \times 2^{-x}
6=2^{x} 7^{x}\left[=14^{x}\right]
\end{array}\)
Use law of the logarithm of a power to solve for \(x\)
Obtain answer \(x=\frac{\ln 6}{\ln 14}\)
Knowledge points:
3.2.3 use logarithms to solve equations and inequalities in which the unknown appears in indices
Solution:
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