solve: for x and y

Question

0.30  = log(x)

 

0.30 = ln(y)

 

log(1.3)=

 

ln(1.3)=

Answer 1

Alan gave you approximations.  In case you need exact solutions (radical form), as sometimes they require, go with these.

 

0.30 = log(x)

 

 

We know that the solution to a log is the exponent to the base number 10.

 

10^0.30 = x

 

 

Rewrite the exponent as a fraction.

 

10^(3/10) = x

 

 

Write the left side as a radical.

 

¹⁰√(10³) = x

 

¹⁰√(1000) = x

 

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0.30 = ln(y)

 

 

The solution to a natural log is the exponent of base number e.

 

e^0.30 = y

 

 

Putting the exponent in fraction form,

 

e^(3/10) = y

 

 

Then in radical form,

 

¹⁰√(e³) = y

 

 

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For the next one, we try to use the properties of logs.

 

log(1.3) =

 

log(1 3/10) =

 

log(13 / 10) =

 

 

Use the difference of logs properties.

 

log(13) - log(10) =

 

log(13) - 1

 

Answer 2

0.30 = log x  ⇒  x = 10^0.30 ≈ 1.995 (to 3 decimal places)

 

0.30 = ln y    ⇒  y = e^0.30 ≈ 1.350

 

log 1.3 ≈ 0.1139  (using a calculator; there is no other way to find it)

 

ln 1.3  ≈ 0.2624   (again, using a calculator)

 

If these answers are not what you need, you need to post a reply so someone can help you further.