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

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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

Mathematics
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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 \[x=\frac{1.169}{2.303}\] \[x= 0.507\]
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let lg logarithm base 10 than lg10^x =3,22lg10 xlg10 = 3,22lg10 x=3,22
0.507856

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