Elementary algebra
Exponential and logarithmic equations

An exponential equation is one which has the form a x = b {\displaystyle a^{x}=b} for a > 0 {\displaystyle a>0}, which has solution

when b > 0 {\displaystyle b>0}. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. For example, if

then, by subtracting 1 from both sides of the equation, and then dividing both sides by 3 we obtain

whence

or

A logarithmic equation is an equation of the form l o g a (x) = b {\displaystyle log_{a}(x)=b} for a > 0 {\displaystyle a>0}, which has solution

For example, if

then, by adding 2 to both sides of the equation, followed by dividing both sides by 4, we get

whence

from which we obtain
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