solvefor y,arcsin(y)=ln(x)

{ "query": { "display": "solve for $$y,\\:\\arcsin\\left(y\\right)=\\ln\\left(x\\right)$$", "symbolab_question": "SOLVE_FOR#solvefor y,\\arcsin(y)=\\ln(x)" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "y=\\sin(\\ln(x))", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$solve\\:for\\:y,\\:\\arcsin\\left(y\\right)=\\ln\\left(x\\right){\\quad:\\quad}y=\\sin\\left(\\ln\\left(x\\right)\\right)$$", "input": "\\arcsin\\left(y\\right)=\\ln\\left(x\\right)", "steps": [ { "type": "interim", "title": "Apply trig inverse properties", "input": "\\arcsin\\left(y\\right)=\\ln\\left(x\\right)", "result": "y=\\sin\\left(\\ln\\left(x\\right)\\right)", "steps": [ { "type": "step", "primary": "$$\\arcsin\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\sin\\left(a\\right)$$", "result": "y=\\sin\\left(\\ln\\left(x\\right)\\right)" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "y", "plotRequest": "\\arcsin(y)-\\ln(x)" }, "showViewLarger": true } }, "meta": { "showVerify": true } }