Question

Convert ln(5x + 7) = 8 into exponent form

Answer 1

Use the property: \(ln~a~=~b;~a~=~e^b\)

Answer 2

\(\bf \large log_{\color{blue}{ b}}=y\implies {\color{red}{ a}}^y={\color{blue}{ b}}\\ \quad \\ \quad \\
ln(5x + 7) = 8\implies log_{\color{red}{ 3}}{\color{blue}{ (5x + 7)}} =8\)

what do you think?

Answer 3

Write the equation e = e
(which is obviously true).

Now let ln(5x+7) be the exponent of the first e and let 8 be the exponent of the 2nd e.

Can you simplify the resulting equation?

Answer 4

3? what the? ahemm \(\large \bf log_{\color{blue}{ b}}=y\implies {\color{red}{ a}}^y={\color{blue}{ b}}\\ \quad \\ \quad \\
ln(5x + 7) = 8\implies log_{\color{red}{ e}}{\color{blue}{ (5x + 7)}} =8\)

Answer 5

5x + 7 = e^8
?

Answer 6

JDoe: how neat your mathematical symbolism is!
I do wonder, however, where that base 3 log came from.

Answer 7

hehehe typo =)

Answer 8

5x + 7 = e^8 \(\large \checkmark\)

Answer 9

Note how JDoe and T have both converted an equation in log form to one in exponential form. That's all we need to do here. It's possible, if you wish, to solve for x, but that was not part of the original question.

Answer 10

ahemm man... I jut noticed more typos... anyway, \(\large \bf log_{\color{red}{ a}}{\color{blue}{ b}}=y\implies {\color{red}{ a}}^y={\color{blue}{ b}}\)

Answer 11

Hey, JDoeTypo, I make my share of typos too. Nice that you're man enough to admit to typos and helpful that you fix them. :)

Answer 12

heheeh