Maths4U Original · Short practice

Let \(\displaystyle a=\)\(3\), \(p = 2187\), \(q = 81\). Work exactly, using index laws.

Find \(\displaystyle \log _{a} p\).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Maths4U Original · Short practice

Let \(\displaystyle a=\)\(4\), \(p = 64\), \(q = 4\). Work exactly, using index laws.

Find \(\displaystyle \log _{a} p\).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Maths4U Original · Short practice

Let \(\displaystyle a=\)\(4\), \(p = 64\), \(q = 4\). Work exactly, using index laws.

Find logₐ(pq).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Maths4U Original · Short practice

Let \(\displaystyle a=\)\(2\), \(p = 16\), \(q = 4\). Work exactly, using index laws.

Find logₐ(pq).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Maths4U Original · Short practice

Let \(\displaystyle a=\)\(e\), \(p = e^{4}\), \(q = e^{2}\). Work exactly, using index laws.

Find \(\displaystyle \log_{a} (\frac{p}{q})\).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Maths4U Original · Short practice

Let \(\displaystyle a=\)\(e\), \(p = e^{7}\), \(q = e\). Work exactly, using index laws.

Find \(\displaystyle \log_{a} (\frac{p}{q})\).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Maths4U Original · Short practice

\(f{\left(x \right)} = 2 \log{\left(3 x - 69 \right)} + 4\), with \(\displaystyle a=3, h=23, b=4\).

Find the gradient where \(\displaystyle a(x-h)=1\).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Maths4U Original · Short practice

\(f{\left(x \right)} = 3 \log{\left(4 x - 96 \right)} + 5\), with \(\displaystyle a=4, h=24, b=5\).

Find the gradient where \(\displaystyle a(x-h)=1\).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.