For all such that

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

For all xx such that sin⁡x>0\sin x>0, which of the following identities is correct? (a) (sin⁡x)x=exsin⁡x(\sin x)^x = e^{x\sin x} (b) (sin⁡x)x=e(ln⁡x)sin⁡x(\sin x)^x = e^{(\ln x)\sin x} (c) (sin⁡x)x=exln⁡(sin⁡x)(\sin x)^x = e^{x\ln(\sin x)} (d) (sin⁡x)x=eln⁡(sin⁡xx)(\sin x)^x = e^{\ln\left(\dfrac{\sin x}{x}\right)}

Related theory

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