Question 239148
{{{(9/2)*log(4, (x)) = 5}}}
Solving logarithmic equations where the variable is in the argument of a logarithm is often done by transforming the equation into one of the following forms:
log(expression-with-variable) = other-expression
or
log(expression-with-variable) = log(other-expression)
The transformations can be done using basic Algebra and/or the properties of logarithms.<br>
For your equation all we need to do to achieve one of these forms is to eliminate the 9/2. The easiest to to this is to multiply both sides of the equation by its reciprocal, 2/9:
{{{(2/9)(9/2)*log(4, (x)) = (2/9)5}}}
which simplifies to
{{{log(4, (x)) = 10/9}}}
which fits the first of the desired forms. To solve equations in this form we use the fact that {{{log(a, (p)) = q}}} is equivalent to {{{p = a^q}}} to rewrite the equation in exponential form:
{{{x = 4^(10/9)}}}
Using a calculator on the right side we get:
{{{x = 4.6661161583044663}}}
(Round this off as desired.)