Question

Please help!! solve the exponential equation. Express the solution in terms of natural logarithms. Then use a calculator to obtain decimal approximation for the solution.
what is the solution in terms of natural logarithms? 10^x = 3.22
what is the solution set

Answer 1

we have got
\[10^x= 3.22\]
take natural logarithm both sides
\[\ln{10^x}=\ln{3.22}\]
we know that log a^x= x log a, ( irrespective of the base)
so
we get
\[x \ln 10= \ln 3.22\]
so
we get
\[ x= \frac{\ln 3.22}{\ln 10}\]
this is the solution in terms of natural logarithm
Using calculator
we get
ln 3.22= 1.169
ln 10= 2.303
so
\[x=\frac{1.169}{2.303}\]
\[x= 0.507\]

Answer 2

heaven did you get this

Answer 3

yes thank you

Answer 4

let lg logarithm base 10
than lg10^x =3,22lg10
xlg10 = 3,22lg10
x=3,22

Answer 5

0.507856