The graph of y=`log_(5)x and y="ln "0.5x` intersect at a point where x equals

Options

A. 6.24
B. 5.44
C. 1.69
D. 1.14

Answer

A

Explanation

Use the change of base formula and graph `y=(logx)/(log5)` as `Y_(1)`. Graph `y=ln(0.5x)`
as `Y_(2)`. The answer choices suggest a [0,10] by [0,2] window. Use the CALC/intersect
As alternative solutio converts the equations to exponential form: `x=5^(y)` and `(1)/(2)x=e^(y),` or `5^(y)=2e^(y)`. taking the natural log of both sides gives `yln5=ln2+y`, and solving for y yields `y=(ln2)/(ln5-1)~~1.14`. finally substituting back to find x,
`5^(1.14)~~6.24`