L2 Algebra
Question Bank
Solve for $x$ in the equation $\log_2(x) = 4$.
Find the value of $m$ if $\log_3(2m-5) = 2$.
Solve the following equation for x: $\log_x(64) = 3$.
Simplify fully: $4\log(y^2) - \log(y^5)$.
Find the value of the expression: $2\log_5(125) - \log_5(\frac{1}{25})$
Solve the equation
$\log_2 x + \log_2 8 = 7$
Without using a calculator, find the exact value of
$\log_4 48 - \log_4 3$
Find the value of $\log_{\sqrt{7}}(\frac{1}{49})$. You must show some algebraic procedure.
Simplify fully $\frac{5\log(u^4)}{\log u}$.
Simplify the following expression fully, writing your answer as a single logarithm: $\log(4a) + 2\log(\frac{a}{8})$.
Solve the equation
$3^{x + 1} = 7^x$
Give your answer correct to 3 decimal places.
Solve the equation
$\log x + \log(x - 3) = 1$
where $\log$ means $\log_{10}$.
The magnitude, $M$, of an earthquake is measured on the Richter scale using the formula $M = \log_{10}(\frac{I}{I_0})$, where $I$ is the intensity of the earthquake and $I_0$ is a reference intensity. An earthquake in City A has a magnitude of 7.2. An earthquake in City B has a magnitude of 5.6. How many times more intense was the earthquake in City A compared to the one in City B?
Solve the equation $(\log_2 x)^2 + \log_2 (x^3) = 10$.
Find the value of x if $2\log_3(x) - \log_3(x+2) = 1$.
Solve the following system of simultaneous equations for $x$ and $y$.
$\log_2(x) + \log_2(y) = 5$ $\log_2(x^3) - \log_2(y^2) = 5$Let $p = \log_2 x$ and $q = \log_2 y$.
(a) Show that
$\log_2\left(\frac{8x^2}{\sqrt{y}}\right) = 3 + 2p - \frac{q}{2}$
(b) Hence, given that $xy = 32$ and $\dfrac{8x^2}{\sqrt{y}} = 256$, find the values of $x$ and $y$.