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PSLE

PSLE Foundation Mathematics

To determine unique constants $x,y$, interpret the equality as an identity for all independent positive bases $m,n$. For fixed unspecified $m,n$, one equation generally does not determine both unknowns.
If&nbsp;$\frac{m^x}{n^y} \times \frac{n^{4-3x}}{(m^{y+1})^2} = \frac{n^7}{m^{10}}$, find the value(s) of $x$ and $y$.

To determine unique constants $x,y$, interpret the equality as an identity for all independent positive bases $m,n$. For fixed unspecified $m,n$, one equation generally does not determine both unknowns.

If $\frac{m^x}{n^y} \times \frac{n^{4-3x}}{(m^{y+1})^2} = \frac{n^7}{m^{10}}$, find the value(s) of $x$ and $y$.

Simultaneous Exponential Equations

Indices

Exponential and Logarithmic Functions

Solve the simultaneous equations.
$x-2y=8$ $3^x(27^y)=9$

Given that&nbsp;$63^x = 35^y = 2205$, find the value of $\frac{x + 4xy + y}{2xy - x - y}$.

Given that $63^x = 35^y = 2205$, find the value of $\frac{x + 4xy + y}{2xy - x - y}$.

IP2U9 HOT Q2

Given that&nbsp;$5^x = 9^y = 2025$, find the value of $\frac{xy}{x + y}$.

Given that $5^x = 9^y = 2025$, find the value of $\frac{xy}{x + y}$.

IP2U9 HOT Q1

Solve the simultaneous equations.
$5^{2x}(5^{6y}) = \frac{1}{25}$
$ \quad\,\,\, \frac{7^x}{49^y} = 7^{-2}$

Solve the following simultaneous equations,
$5^x (125)^{2y} = 1$
$\frac{9^y}{\sqrt{3^x}} = \frac{1}{729}$

Solve the following simultaneous equations,

Solve the following simultaneous equations:
$2^x + 3^y = 43$
$2^{x+1} + 3^{y+2} = 275$

Solve the following simultaneous equations:

Solve, for&nbsp;$x$ and $y$, in the following simultaneous equations:
$5^{2x} \times 5^y = 125$
$2^{4x} \div 2^{2y} = 16^{-1}$

Solve, for $x$ and $y$, in the following simultaneous equations:

Without using a calculator, solve for&nbsp;$x$ and $y$, in the following simultaneous equations:
$\frac{4^x}{8^{y+1}} = 1$
$9^{x-1} = 27^{2y}$

Without using a calculator, solve for $x$ and $y$, in the following simultaneous equations:

Without using a calculator, solve, for&nbsp;$x$ and $y$, in the following simultaneous equations:
$ \qquad\,\,\,8^x \div 2^y = 64$
$3^{4x} \times \left(\frac{1}{9}\right)^{y-1} = 81$

Without using a calculator, solve, for $x$ and $y$, in the following simultaneous equations:

$3^{4x} \times \left(\frac{1}{9}\right)^{y-1} = 81$

Solve the simultaneous equations:
$4^x (2^y) = \frac{2^{11}}{16^y}$
$5^x (5^{x-6y}) = 1$

Solve the following simultaneous equations.
${\log_{2}(x - y) - \log_{2}(y + 4) = 2}$
${ \: 25^{x}(5^{y}) = 0.2}$

Solve the following simultaneous equations.

${\log_{2}(x - y) - \log_{2}(y + 4) = 2}$

Solving Logarithm Equations

Solve the simultaneous equations.
${ \, \frac{3^{x+1}}{3^{y}} = 9}$
${\ln(6x + 3y) = 3\ln 2 + \ln 3}$

Solve the simultaneous equations.
${e^{2}e^{x} = e^{4y}}$
${\log_{4}(x + 2) = 1 + \log_{2}y}$

Solve the simultaneous equations.
${\log_{4}x - \log_{2}y = 2}$
${ \,\,\, 3^{x} = 81\left(9^{\frac{3}{2} - 3y}\right)}$

${ \,\,\, 3^{x} = 81\left(9^{\frac{3}{2} - 3y}\right)}$

Simultaneous Equations

Solve the following simultaneous equations,
${5^{x}(125)^{2y} = 1}$
${ \qquad\;\;\;\;\, \frac{9^{y}}{\sqrt{3^{x}}} = \frac{1}{729}}$

${ \qquad\;\;\;\;\, \frac{9^{y}}{\sqrt{3^{x}}} = \frac{1}{729}}$

Solve the following simultaneous equations:
${ \quad\, 2^{x} + 3^{y} = 43}$
${2^{x+1} + 3^{y+2} = 275}$

Solve, for&nbsp;$x$ and $y$, in the following simultaneous equations:
${5^{2x} \times 5^{y} = 125}$
${2^{4x} \div 2^{2y} = 16^{-1}}$

Without using a calculator, solve for&nbsp;$x$ and $y$, in the following simultaneous equations:
${\frac{4^{x}}{8^{y+1}} = 1}$ 
${ \quad 9\;\;\,^{x-1} = 27^{2y}}$

Without using a calculator, solve, for $x$ and $y$, in the following simultaneous equations:
${\frac{8^x}{2^y} = 64}$
${3^{4x} \times \left(\frac{1}{9}\right)^{y - 1} = 81}$

${3^{4x} \times \left(\frac{1}{9}\right)^{y - 1} = 81}$

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