solve 4^xe^(7x+5) = 21
ln((4^x)e^(7x+5)) = ln21; apply a natural log on both sides of the equation as an exponential containing e is involved
ln4^x + ln(e^(7x+5)) = ln21; using logarithm rules you can seperate the single log on the LHS to form to logs as ln(ab) = lna + lnb
xln4 + 7x + 5 = ln21; using logarithm rules we can move down the power on the ln4e^x and lne^(7x+5) and since lne is 1 we are left with xln4+7x+5
x(ln4 + 7) = ln21 - 5; factor out the variable components and move all numbers with no variable to the same side of the equation
x = (ln21-5)/(ln4+7); divide through by the coefficient of x
WN
Related Maths A Level answers
All answers ▸What is the derivative with respect to x of the function f(x)=1+x^3+ln(x), x>0 ?
Differentiate the function X^4 - (20/3)X^3 + 2X^2 + 7. Find the stationary points and classify.
Finding the tangent of an equation using implicit differentiation
how can differentiate using the product and chain rule? e.g y=(4x+1)^3(sin2x), find dy/dx.