Moderate -0.3 This is a standard quadratic-in-disguise problem requiring substitution u=3^x, solving the resulting quadratic, then taking logarithms. It's a routine textbook exercise with a well-known technique, making it slightly easier than average, though the logarithm step adds minor computational complexity beyond pure algebraic manipulation.
Carry out recognizable solution method for quadratic in \(3^x\)
M1
Obtain \(3^x = 5\) and \(3^x = 2\)
A1
Use logarithmic method to solve an equation of the form \(3^x = k\), where \(k > 0\)
M1
State answer 1.46
A1
State answer 0.631
A1
[5]
Carry out recognizable solution method for quadratic in $3^x$ | M1 |
Obtain $3^x = 5$ and $3^x = 2$ | A1 |
Use logarithmic method to solve an equation of the form $3^x = k$, where $k > 0$ | M1 |
State answer 1.46 | A1 |
State answer 0.631 | A1 | [5]