Let $L$ be the Lazard's universal ring, and $R=\mathbb{Z}[b_1,b_2,\cdots,b_n,\cdots]$, regarded as a graded ring with the degree of $b_i$ equal to $2i$. Let $\theta: L\rightarrow R$ be the homomorphism carrying the universal formal group law $\mu^L$ to the formal group law $$\mu^R(x_1,x_2)=\exp(\log(x_1)+\log(x_2)),$$ where the power series $$\exp(x)=x+\sum_{i\geq 1}b_ix^{i+1},$$ and $\log(x)$ its inverse, denoted as $$\log(x)=x+\sum_{i\geq 1}m_ix^{i+1}.$$ Let $MU$ be the complex cobordism spectrum, and by Quillen's theorem we have the following commutative diagram $\require{AMScd}$ \begin{CD} L @>\theta>> R\\ @V \cong V V @VV \cong V\\ \pi_*(MU) @>>h> H_*(MU;\mathbb{Z}) \end{CD}

where $h$ is the Hurewicz homomorphism.

In Section 9, Part II of

*Adams, J. F.*, Stable homotopy and generalised homology, Chicago Lectures in Mathematics. Chicago - London: The University of Chicago Press. X, 373 p. 3.00 (1974). ZBL0309.55016.**

it is stated that the class $[\mathbb{C} P^n]\in\pi_*(MU)$ is sent to $(n+1)m_n\in H_*(MU;\mathbb{Z})$ by $h$, and it is indicated there that the argument is a Chern number computation, but I am not seeing the argument.**

I would greatly appreciate your help if you could sketch the proof or point out a reference containing a proof. Thank you!