Exponentials & Logs (DP IB Analysis & Approaches (AA): SL): Exam Questions

Let $f\left(x\right)=5\ln \left(x-7\right)$.

Find the values of $x$ for which $f\left(x\right)$ is undefined.

Given that point $\mathrm{P}$ has coordinates $\left(p,0\right)$, find the value of $p$.

Given that $2^m=8$ and $2^n=16$, write down the value of $m$ and of $n$. 

Hence or otherwise solve $8^{2?+1}={16}^{2?-3}$.

Write the expression $3\ln 2-\ln 4$ in the form $\ln k$, where $k\in \mathrm{\mathbb{Z}}$.

Hence, or otherwise, solve $3\ln 2-\ln 4=-\ln x$.

Solve the equation ${49}^{p+4}={35}^{2p}$ for $p$. Express your answer in terms of $\ln 7$ and $\ln 5$.

Solve the equation $4^x-3\times 2^{x+2}=64$.

It is given that $p=lo{g}_{124}125\times lo{g}_{123}124\times lo{g}_{122}123\times \dots \times lo{g}_{5}6$.

Given that $p\in \mathrm{\mathbb{Z}}$, find the value of $p$.

Solve the equation  ${\log }_{6}3+{\log }_{6}2x=2-{\log }_{6}12$.

Solve the equation ${\log }_{9}x-{\log }_{9}2=2+{\log }_{9}5$.

Find the value of ${\log }_{4}32+{\log }_{4}8$.

Find the value of ${64}^{{\log }_{4}3}$.

Find the integer values of $x$ and$y$ for which $x+y{\log }_{9}5+12{\log }_{27}15=0$

Let $f\left(x\right)=\ln \left(\frac{x}{3}-1\right).$

Find the values of $x$ for which$f\left(x\right)$ is undefined.

Given that point has A coordinates $\left(a,0\right)$, find the value of $a$.

Solve ${27}^{4x+2}={81}^{8x-3}.$

Solve $5\ln 2-\ln 8=-\ln x.$

Solve the equation ${216}^{k+2}={12}^{3k}$ for $k$. Express your answer in terms of $\ln 6$ and $\ln 2.$

Solve the equation $2\times {25}^x-30\times 5^{x-1}=1.$

It is given that$p={\log }_{242}243\times {\log }_{241}242\times {\log }_{240}241\times ...\times {\log }_{3}4.$

Given that$p\in \mathrm{\mathbb{Z}},$ find the value of$p.$

Solve the equation ${\log }_{5}x-{\log }_{5}4=4+{\log }_{5}2.$

Solve the equation ${\log }_4\left(2-x\right)={\log }_{16}\left(13-4x\right).$

Find the value of ${\log }_{8}2560-{\log }_{8}5.$

Find the value of ${64}^{{\log }_{8}5}.$

Find the integer values of $x$ and $y$ for which $x+y{\log }_{343}6-10{\log }_{49}42=0$