Rewrite the equation in terms of base e.

Question

Rewrite the equation in terms of base

e.

Express the answer in terms of a natural logarithm and then round to three decimal places.

y=101(4.8)x

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Part 1

Express the answer in terms of a natural logarithm.

y=___________​(Do not​ simplify.)

Part 2

Simplify the​ answer, rounding to three decimal places.

y=___________

Answer 1

4.8 = about e^1.569

101=about e^4.615

y =101(4.8)^x = 101(e^1.569)^x

y = 101e^1.569x

y= (e^4.615)(e^1.569x)

y= e^(4.615+1.569x)

lny = 4.615+1.569x

y =101(4.8)^x

y/101 = 4.8^x

ln(y/101) = xln4.8

lny-ln101 = xln4.8

lny = xln4.8 +ln101

lny = ln(101(4.8)^x)

y = e^ln(101(4.8)^x)

y = 101(4.8)^x

although the quesiton is somewhat mysterious, and unclear.

"base" sorts to seem like the base of a triangle rathr than the base of an exponential function.

but the above is maybe a few helpful use of logs and exponsent properties.