Question

$\boxed{solve\:for\:x,\:\:e^{4x}=16}$

solve it!!!.

Challenge for stars and mods or future star

Answer 1

Explanation:

ANSWER

4x

3

+16x

2

−9x−36=0

Let the roots be a,−a,b

a−a+b=−

4

16

=−4

⇒b=−4

a(−a)+(−a)b+ab=

4

−9

a

2

=

4

9

⇒a=±

2

3

So the roots of the equation are

2

3

,−

2

3

,−4

Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\bf{Find\:\:x\:\:in\:\::\:e^{4x}=16$

♣ ᴀɴꜱᴡᴇʀ :

$\bf{{If\:}f\left(x\right)=g\left(x\right)}\bf{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)}$

$\bf{ln \left(e^{4x}\right)=\ln \left(16\right)}$

$\bf{{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)}$

$\bf{ln \left(e^{4x}\right)=4xln \left(e\right)}$

$\bf{4x\ln \left(e\right)=\ln \left(16\right)}$

$\bf{\bf{{Apply\:log\:rule}:\quad \log _a\left(a\right)=1}}$

$\bf{\ln \left(e\right)=1}$

$\bf{4x=\ln \left(16\right)}$

$\boxed{\bf{x=ln \left(2\right)}}$