G(x)=x^3 + 1, h(x)=3^x; solve G(h(a))=244

First combine the two functions so that we have an equation for a to solve:

G(h(a)) = (3^x)^3 + 1 = 3^(3x) + 1 = 244

which gives

3^(3x) = 243

Now we can use logarithms in order to solve the equation

log(3^(3x)) = log(243)

but log(3^(3x))=3x*log(3)

so we have x = (log(243))/(3*log(3))

and if we enter this into a calculator we find that x=5/3

JS
Answered by Josephine S. Maths tutor

4206 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the area enclosed between C, the curve y=6x-x^2, L, the line y=16-2x and the y axis.


How do I do definite integrals?


Differentiate (3x^2-5x)/(4x^3+2x^2)


Differentiate with respect to x, x^2*e^(tan(x))


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences