CHO F X ( ) = A LN ( X + X2+ + 1 ) B SIN X + 6 V Ớ I , A B ∈ R

Câu 30: Cho ^{f x ( ) = a ln} ( ^{x + x}

^{+ + 1} ) ^{b sin x + 6 v ớ i , a b ∈ R . Bi ế t f ( log log ( e ) ) = 2.} Tính giá tr ị c ủ a

( ^{log ln10} )

( )

f .

A. 4. B. 10. C. 8. D. 2.

L ờ i gi ả i

Chú ý rằng log log ( e ) + log ln10 ( ) = log log .ln10 ( e ) = log log (

e .log 10

) = log 1 ( ) = 0 .

Đặt ^{log log} ( ^e ) ^{= ⇒ t log ln10} ( ) ^{= − t .}

Ta có: ^{f t ( ) = a ln} ( ^{t + t}

^{+ + 1} ) ^{b sin t + = ⇒ 6 2 a ln} ( ^{t + t}

^{+ + 1} ) ^{b sin t = − 4 .}

(

) ^{( )}

(

)

( ) ln 1 sin 6 ln 1 sin 6 ln 1 sin 6

− = − + + + − + = − + = − + + − +

f t a t t b t a b t a t t b t

+ +

1

t t

= + = . Ch ọ n B.

4 6 10