17c6e2…: “After the red castle”

$\newenvironment {prompt}{}{} \newcommand {\ungraded }[0]{} \newcommand {\HyperFirstAtBeginDocument }[0]{\AtBeginDocument }$

1 : Solve for $x$ in the following exponential equation: $\left (\sage {p1b2}\right )^{\sage {p1f1}} = \left (\sage {p1b3}\right )^{\sage {p1f2}}$

$x = \answer {\sage {p1ans1}}$ .

You want to rewrite everything so that it is the same base. For example, you can write $\sage {p1b2} = \sage {p1b1}^{\sage {p1pwr1}}$ and $\sage {p1b3} = \sage {p1b1}^{\sage {p1pwr2}}$ . Then use the fact that if both sides have the same base, their exponents must be equal (the one to one property of exponents) to get an equation you can solve.

2 : Solve for $x$ in the following exponential equation: $\left (\sage {p2b2}\right )^{\sage {p2f1}} = \left (\sage {p2b3}\right )^{\sage {p2f2}}$

$x = \answer {\sage {p2ans1}}$ .

You want to rewrite everything so that it is the same base. For example, you can write $\sage {p2b2} = \sage {p2b1}^{\sage {p2pwr1}}$ and $\sage {p2b3} = \sage {p2b1}^{\sage {p2pwr2}}$ . Then use the fact that if both sides have the same base, their exponents must be equal (the one to one property of exponents) to get an equation you can solve.

3 : Solve for $x$ in the following exponential equation: $\left (\sage {p3b2}\right )^{\sage {p3f1}} = \left (\sage {p3b3}\right )^{\sage {p3f2}}$

$x = \answer {\sage {p3ans1}}$ .

You want to rewrite everything so that it is the same base. For example, you can write $\sage {p3b2} = \sage {p3b1}^{\sage {p3pwr1}}$ and $\sage {p3b3} = \sage {p3b1}^{\sage {p3pwr2}}$ . Then use the fact that if both sides have the same base, their exponents must be equal (the one to one property of exponents) to get an equation you can solve.

4 : Solve for $x$ in the following exponential equation: $\left (\sage {p4b2}\right )^{\sage {p4f1}} = \left (\sage {p4b3}\right )^{\sage {p4f2}}$

$x = \answer {\sage {p4ans1}}$ .

You want to rewrite everything so that it is the same base. For example, you can write $\sage {p4b2} = \sage {p4b1}^{\sage {p4pwr1}}$ and $\sage {p4b3} = \sage {p4b1}^{\sage {p4pwr2}}$ . Then use the fact that if both sides have the same base, their exponents must be equal (the one to one property of exponents) to get an equation you can solve.

Press...	...to do
left/right arrows	Move cursor
shift+left/right arrows	Select region
ctrl+a	Select all
ctrl+x/c/v	Cut/copy/paste
ctrl+z/y	Undo/redo
ctrl+left/right	Add entry to list or column to matrix
shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
ctrl+up/down	Add row to matrix
shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
norm	$\|\|\blue{[?]}\|\|$
text	$\text{\blue{[?]}}$
sym_name	$\backslash\texttt{\blue{[?]}}$
abs	$\left\|\blue{[?]}\right\|$
sqrt	$\sqrt{\blue{[?]}}$
paren	$\left(\blue{[?]}\right)$
floor	$\lfloor \blue{[?]} \rfloor$
factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
cot	$\cot\left(\blue{[?]}\right)$
log	$\log\left(\blue{[?]}\right)$
ln	$\ln\left(\blue{[?]}\right)$
alpha	$\alpha$
beta	$\beta$
gamma	$\gamma$
delta	$\delta$
epsilon	$\epsilon$
zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

Controls

Symbols

Settings