Question 183941
please solve for x
log cube root of x = square root of log x
:
You can write it using exponent for cube root
{{{log(x^(1/3)) = sqrt(log(x))}}}
log equiv of exponent
{{{(1/3)log(x) = sqrt(log(x))}}}
:
Let r = log(x) and rewrite the above equation using r
{{{(1/3)r = sqrt(r)}}}
Multiply both sides by 3
{{{r = 3*sqrt(r)}}}
square both sides
r^2 = 9r
divide both sides by r
r = 9
:
replacing r with log(x): 
log(x) = 9
find the {{{10^x}}} of 9
x = 1,000,000,000
;
:
Check for equality on a calc:
enter: log(1000000000^(1/3)) = 3
and
enter: {{{sqrt(log(1000000000))}}} = 3 also