Find the solution of 3^{4x} = 9^{(x-1)/2}.
First, recognise that 3^2 = 9. Recall the rule for multiplying indices, that (a^b)^c = a^{bc}. Then, substitute 3^2 in place of 9 to get 3^{4x} = (3^2)^{(x-1)/2}. Use the rule for multiplying indices, so that the equation is now 3^{4x} = 3^{x-1}. This implies 4x=x-1, and therefore 3x = -1, and finally, x = -1/3 is the solution.
CO
Answered by Charles O. • Further Mathematics tutor
2640 Views
See similar Further Mathematics GCSE tutorsRelated Further Mathematics GCSE answers
All answers ▸The circle c has equation x^2+ y ^2=1 . The line l has gradient 3 and intercepts the y axis at the point (0, 1). c and l intersect at two points. Find the co-ordinates of these points.
If z=4+i, what is 1/z? (in the form a+bi)
How would I solve the following equation d^2x/dt^2 + 5dx/dt + 6x = 0
Point A lies on the curve: y=x^2+5*x+8. The x-coordinate of A is -4. What is the equation of the normal to the curve at A?