Question 1076076

solve each equation by first rewriting the expression in each part with the same base
c. 4^2x=(1/2)^x+5
<pre>{{{matrix(1,3, 4^(2x), "=", (1/2)^(x + 5))}}}
{{{matrix(1,3, 2^(4x), "=", (2^(- 1))^(x + 5))}}} ------ Converting {{{matrix(1,5, 4^(2x), "=====>", (2^2)^(2x), "=====>", 2^(4x))}}} and {{{matrix(1,3, 1/2, to, 2^(- 1))}}}
{{{matrix(1,3, 2^(4x), "=", 2^(- 1(x + 5)))}}}
4x = - 1(x + 5) ------- Bases are equal and so are the exponents
4x = - x - 5
4x + x = - 5
5x = - 5
{{{highlight_green(matrix(1,5, x, "=", (- 5)/5, or, - 1))}}}