Question 473154
1)  {{{log(5,(x^2-2x-10))= 2}}} Convert this equation to an exponential.
{{{5^2=x^2-2x-10}}} Solve this quadratic
{{{25=x^2-2x-10}}}
{{{0=x^2-2x-35}}}
{{{0=(x-7)(x+5)}}}
{{{x=7}}}{{{x=-5}}}

2)   {{{2^(3x-7)=8^(2x+2)}}} Try to get the bases to be equal. Change 8 to {{{2^3}}}
{{{2^(3x-7)=2^(3(2x+2))}}} Distribute the 3
{{{2^(3x-7)=2^(6x+6)}}} Remove bases. Once the bases are the same, the exponents equal each other
{{{3x-7=6x+6}}} Solve for x.
{{{-13=3x}}}
{{{x=-13/3}}}

3)   {{{x=log(sqrt(2),sqrt(512))}}} not sure if this is what you meant
Change to an exponential equation
{{{sqrt(2)^x=sqrt(512)}}} Change 512 to something with a base of 2. Also change square roots into rational exponents
{{{2^((1/2)*x)=512^(1/2)}}}
{{{2^((1/2)*x)=2^(9*(1/2))}}} Now remove the bases since they are the same.
{{{(1/2)x=9(1/2)}}} Solve for x.
{{{x=9}}}

4)   {{{7^x = 1/343}}} Try to get 343 into a base of 7
{{{7^x=343^-1}}}
{{{7^x=7^(3*-1)}}}
{{{7^x=7^-3}}}
{{{x=-3}}}

5)   {{{2x + y^2 - 6y - 12 = 0 }}} What are the directions?