Question

Sa se rezolve ecuatile:

5 * 3 ^ x - 2 * 3 ^ x = 81

2 ^ x * 3 ^ (x + 2) = 54

x ^ 2 + 10 ^ 100 = 10 ^ 101
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Answer 1

Explicație pas cu pas:

$5 \cdot {3}^{x} - 2 \cdot {3}^{x} = 81$

$3 \times {3}^{x} = {3}^{4} \iff {3}^{x + 1} = {3}^{4}$

$x + 1 = 4 \implies x = 3$

.

${2}^{x} \cdot {3}^{x + 2} = 54$

${3}^{2} \cdot {2}^{x} \cdot {3}^{x} = 54$

$9 \cdot {(2 \cdot 3)}^{x} = 54$

${6}^{x} = 6 \iff {6}^{x} = {6}^{1}$

$\implies x = 1$

.

${x}^{2} + {10}^{100} = {10}^{101}$

${x}^{2} = {10}^{101} - {10}^{100}$

${x}^{2} = {10}^{100}(10 - 1)$

${x}^{2} = 9 \cdot {10}^{100} \iff {x}^{2} = {3}^{2} \cdot {( {10}^{50} )}^{2}$

${x}^{2} = {({3} \cdot {10}^{50} )}^{2} \implies x = {3} \cdot {10}^{50}$