Question 203958
1. Make t the subject of the equation y = sqrt(8t + 3)
y = {{{sqrt(8t+3)}}}
Square both sides:
y^2 = 8t + 3
Subtract 3 from both sides
y^2 - 3 = 8t
Divide both sides by 8
{{{(y^2-3)/8}}} = t

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2. Make x the subject of the equation y = 3e^(2x)
y = {{{3*e^(2x)}}}
Divide both sides by 3
{{{y/3}}} = {{{e^(2x)}}}
find the natural log of both sides
{{{ln(y/3)}}} = {{{ln(e^(2x))}}}
log equiv of exponents:
{{{ln(y/3)}}} = {{{2x*ln(e)}}}
natural log of e is 1
{{{ln(y/3)}}} = 2x
divide both sides by 2
{{{(ln(y/3))/2}}} = x