Respuesta :

In [tex]e^{2x} =10[/tex] , x = 1., by the properties of logarithm.

What is Logarithm?

  • The opposite of exponentiation is the logarithm.
  • This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.
  • A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Now,

In [tex]e^{2x} =10[/tex] , taking natural logarithm on both side.

=>  [tex]log_e(e^{2x})=log_e(10)[/tex]

By properties of logarithm, we know that: [tex]log_b(a)^m = m(log_b(a))[/tex]

=> [tex]2x(log_e(e))=ln(10)[/tex]

Also, as [tex]log_e(e)[/tex] = 1,

=> 2x (1) = ln(10)

=> 2x = 2.302 (approx)

=> x = 1.151

Hence, In [tex]e^{2x} =10[/tex] , x = 1.151, by the properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

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