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.

Related Further Mathematics GCSE answers

All answers ▸

Find the definite integral of f(x) = 12/(x^2+10x+21) with limits [-1,1]. Give your answer to 2 decimal places.


Find the coordinates of the minimum/maximum of the curve: Y = 8X - 2X^2 - 9, and determine whether it is a maximum or a minimum.


Find the General Second Order Differential Equation Using Substitution (A2 Further Maths)


Plot the graph of 1/x for x greater than 0.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences