## anonymous 4 years ago 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

1. ash2326

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 $x=\frac{1.169}{2.303}$ $x= 0.507$

2. ash2326

heaven did you get this

3. anonymous

yes thank you

4. jhonyy9

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

5. anonymous

0.507856