# How do you solve #11.3^(2x – 1) = 15.7#?

I found:

In this case, I would make use of one logarithmic property (relating to the argument's exponent) and the natural log on both sides:

I write:

then:

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To solve (11.3^{2x - 1} = 15.7), you can use logarithms. Taking the logarithm of both sides, specifically the natural logarithm (ln), we can solve for (x). After applying logarithms, the equation becomes:

[2x - 1 = \frac{\ln(15.7)}{\ln(11.3)}]

Then, solve for (x) by isolating it:

[2x = \frac{\ln(15.7)}{\ln(11.3)} + 1]

[x = \frac{1}{2}\left(\frac{\ln(15.7)}{\ln(11.3)} + 1)]

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