Moderate -0.8 This is a straightforward exponential equation requiring taking logarithms of both sides and rearranging to solve for x. It's a standard textbook exercise with a clear method (take logs, use log laws, collect x terms, solve) requiring no problem-solving insight, making it easier than average but not trivial since it involves algebraic manipulation with logarithms.
Use law for the logarithm of a product, power or quotient
M1*
Obtain a correct linear equation, e.g. \((2x-1)\ln 5 = \ln 2 + x \ln 3\)
A1
Solve a linear equation for \(x\)
M1(dep*)
Obtain answer \(x = 1.09\)
A1
[4]
[SR: Reduce equation to the form \(a^x = b\) M1*, obtain \(\left(\frac{25}{3}\right)^x = 10\) A1, use correct method to calculate value of \(x\) M1(dep*), obtain answer 1.09 A1.]
Use law for the logarithm of a product, power or quotient | M1* |
Obtain a correct linear equation, e.g. $(2x-1)\ln 5 = \ln 2 + x \ln 3$ | A1 |
Solve a linear equation for $x$ | M1(dep*) |
Obtain answer $x = 1.09$ | A1 | [4]
[SR: Reduce equation to the form $a^x = b$ M1*, obtain $\left(\frac{25}{3}\right)^x = 10$ A1, use correct method to calculate value of $x$ M1(dep*), obtain answer 1.09 A1.] |