Question

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Answer 1

$\huge \tt \underline \orange {Question}$

Solve the Value for x

1. $\tt (\frac{4}{3} ) ^{ - 4} \times (\frac{4}{3} ) ^{ - 5} = (\frac{4}{3} ) ^{ - 3}$
2. $\tt {7}^{x} \div {7}^{ - 3} = { {7}^{5} }$
3. $\tt(4 {)}^{2x + 1} \div 16 = 64$
4. $\tt {2}^{x + 4} - {2}^{x + 2} = 3$
5. $\tt{2}^{x} - {2}^{x - 1} = 4$
6. $\tt( \frac{4}{5} ) ^{2x - 1} \div (\frac{4}{5} )^{ - 2} = (\frac{4}{5} ) ^{3x}$

$\huge \tt \underline \orange {Answer}$

$\tt \red {Answer \: 1st}$

$\tt \implies (\frac{4}{3} ) ^{ - 4} \times (\frac{4}{3} ) ^{ - 5} = (\frac{4}{3} ) ^{ - 3}$

$\tt \implies( \frac{3}{4} ) ^{4} \times ( \frac{3}{4} ) ^{5} = ( \frac{3}{4} ) ^{3x} \\ \\ \tt \implies ( \frac{3}{4} ) ^{4 + 5} = ( \frac{3}{4} ) ^{3x} \\ \\ \tt \implies( \frac{3}{4} ) ^{9} = ( \frac{3}{4} ) ^{3x} \\ \\ \tt \longrightarrow9 = 3x \\ \\ \tt \implies3x = 9 \\ \\ \tt \implies x = \cancel{ \frac{9}{3} } \\ \\ \tt \implies x = 3$

$\tt \red {Answer \: 2nd}$

$\tt\implies {7}^{x} \div {7}^{ - 3} = { {7}^{5} }$

$\tt \implies {7}^{ - 3} = {7}^{5} \\ \\ \tt \implies x - 3 = 5 \\ \\ \tt \implies x = 8$

$\tt \red {Answer \: 3rd}$

$\tt \implies (4 {)}^{2x + 1} \div 16 = 64$

$\tt \implies {2}^{x + 4} - {2}^{x + 2} = 3$

$\tt \implies(4 {)}^{2x + 1} \div {4}^{2} = {4}^{3} \\ \\ \tt \implies(4 {)}^{2x + 1 - 2} = {4}^{3} \\ \\ \tt \implies(4 {)}^{2x - 1}= {4}^{3} \\ \\ \bf\longrightarrow 2x - 1 = 3 \\ \\ \tt \implies 2x = 3 + 1 \\ \\ \tt \implies 2x = 4 \\ \\ \tt \implies x = \cancel{ \frac{4}{2} } \\ \\ \tt \implies x = 2$

$\tt \red {Answer \:4th}$

$\tt \implies {2}^{x + 4} - {2}^{x + 2} = 3$

$\tt \implies {2}^{x} \times {2}^{4} - {2}^{x} \times {2}^{2} = 3 \\ \\ \tt \implies {2}^{x} [ {2}^{4} - {2}^{2} ] = 3 \\ \\ \tt \implies {2}^{x}[16 - 4] = 3 \\ \\ \tt \implies {2}^{x} \times 12 = 3 \\ \\ \tt \implies {2}^{x} = \frac{3}{12} \\ \\ \tt \implies {2x}^{ \frac{1}{4} } \\ \\ \tt \implies {2}^{x} = \frac{1}{ {2}^{2} } \\ \\ \tt \implies {2}^{x} = {2}^{ - 2} \\ \\ \tt \implies x = - 2$

$\tt \red {Answer \:5th}$

$\tt \implies{2}^{x} - {2}^{x - 1} = 4$

$\tt \implies {2}^{x} - \frac{ {2}^{x} }{2} = 4 \\ \\ \tt \implies {2}^{x} (1 - \frac{1}{2} ) = 4 \\ \\ \tt \longrightarrow {2}^{x} = 8 \\ \\ \tt \implies {2}^{x} = {2}^{3} \\ \\ \tt \implies {x} = 3$

$\tt \red {Answer \: 6th}$

$\tt \implies ( \frac{4}{5} ) ^{2x - 1} \div (\frac{4}{5} )^{ - 2} = (\frac{4}{5} ) ^{3x}$

$\tt \implies( \frac{4}{5} ) ^{2x - 1 - 2} = ( \frac{4}{5} {)}^{3x} \\ \\ \tt \longrightarrow 2x - 4 = 3x \\ \\ \tt \implies - x= 4 \\ \\ \tt \implies x= - 4$

Answer 2

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