Question

ss="latex-formula">
(a) State the exact answer for x.



(b) State the approximate answer for x rounded to 4 decimal places.


WILL MARK BRAINLIEST IF YOU SHOW ALL WORK

Answer 1

It looks like you tried to write

e^4^x

which I would interpret as either

$e^{4^x}$ (so the exponent on e is 4ˣ )

or

$e^{4x}$ (so the exponent on e is 4x )

as it's shown in the question body.

If you meant the first case,

$e^{4^x}-4=1$

$e^{4^x}=5$

$\ln\left(e^{4^x}\right)=\ln(5)$

$4^x\ln(e)=\ln(5)$

$4^x=\ln(5)$

$\log_4\left(4^x\right)=\log_4\left(\ln(5)\right)$

$x\log_4(4)=\log_4\left(\ln(5)\right)$

$\boxed{x=\log_4\left(\ln(5)\right)}\approx0.3433$

If you meant the second case,

$e^{4x}-4=1$

$e^{4x}=5$

$\ln\left(e^{4x}\right)=\ln(5)$

$4x\ln(e)=\ln(5)$

$4x=\ln(5)$

$\boxed{x=\dfrac{\ln(5)}4\approx0.4024}$