Question 354710
With an equation of the form
log(expression) = other-expression
and the variable in the argument or base of the logarithm, then you will usually rewrite the equation in exponential form. In general, {{{log(a, (p)) = q}}} is equivalent to {{{a^q = p}}}. Using this on your equation we get:
{{{x^(-6) = 64}}}
Rewriting this with a positive exponent we get:
{{{1/x^6 = 64}}}
We can eliminate the fraction by multiplying both sides by {{{x^6}}}:
{{{1 = 64x^6}}}
Next we can divide both sides by 64:
{{{1/64 = x^6}}}
To find x we will find the 6th root of each side:
{{{root(6, 1/64) = root(6, x^6)}}}
(Since x is the base of a logarithm in this problem, we can ignore the negative 6th roots of 64. Bases of logarithms must be positive!) Since {{{2^6 = 64}}} we get 1/2 on the left side:
{{{1/2 = x}}}