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

4155 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate 3x^2+1/x and find the x coordinate of the stationary point of the curve of y=3x^2+1/x


factorise x^3 + 3x^2 - 13x - 15


Integrate ⌠( xcos^2(x))dx


Find the gradient of the curve y = x^2(ln(x)) at x = e


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