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natta225 [31]
3 years ago
8

"absmiddle" class="latex-formula"> (solve with explanation)
Mathematics
1 answer:
KiRa [710]3 years ago
8 0
e ^{2x} = ln5

Solve for the real domain

e ^{2x} = ln(5)

if f(x) =g(x), then ln(f(x))= ln(g(x))

ln(e ^{2x} ) = ln(ln(5))

Solve : <span>ln(e ^{2x} ) = ln(ln(5))
</span>
use the logarithmic definition :

ln(e^{f(x)} ) = f(x)

ln(e^{2x} ) = 2x

2x=ln(ln(5))

Divide both sides by 2 :

\frac{2x}{2} = \frac{ln(ln(5))}{2}

x= \frac{ln(ln(5))}{2}

hope this helps!

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