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Erika is working on solving the exponential equation 50x = 17; however, she is not quite sure where to start. using complete sentences, describe to erika how to solve this equation.

hint: use the change of base formula: log base b of y equals log y over log b.

Sagot :

Erika is working on solving the exponential equation 50^x = 17; The solution is x = 0.7242.

What is logarithm?

When you raise a number with an exponent, there comes a result.

Let's say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Erika is working on solving the exponential equation 50^x = 17;

however, she is not quite sure where to start.

The equation is

[tex]50^x = 17\\[/tex]

By taking the log both sides

[tex]log_a b = x\\\\a_x = b[/tex]

By using the base formula

[tex]log_0 y = \dfrac{logy}{log b}[/tex]

So, [tex]log_{50} 17= x\\\\[/tex]

[tex]x = \dfrac{log17}{log 50}[/tex]

x = 0.7242

Learn more about logarithm here:

https://brainly.com/question/20835449

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