Call Now Button
Други разред средње школе

Експоненцијалне једначине 5

Задаци

Текст задатака објашњених у видео лекцији.

Решити експоненцијалну једначину.

пр.15)   ${6^x} + {6^{x + 1}} = {2^x} + {2^{x + 1}} + {2^{x + 2}}$

пр.16)   ${5^{2x}} - {7^x} - {5^{2x}} \cdot 35 + {7^x} \cdot 35 = 0$

пр.17)   $7 \cdot {3^{x + 1}} - {5^{x + 2}} = {3^{x + 4}} - {5^{x + 3}}$

Пр.15

\[\begin{gathered}
{6^x} + {6^{x + 1}} = {2^x} + {2^{x + 1}} + {2^{x + 2}} \hfill \\
{6^x} + {6^x} \cdot 6 = {2^x} + {2^x} \cdot 2 + {2^x} \cdot {2^2} \hfill \\
{6^x}\left( {1 + 6} \right) = {2^x}\left( {1 + 2 + 4} \right) \hfill \\
{6^x} \cdot 7 = {2^x} \cdot 7 \hfill \\
{6^x} = {2^x}\left| {{2^x}} \right. \hfill \\
\frac{{{6^x}}}{{{2^x}}} = 1 \hfill \\
{\left( {\frac{6}{2}} \right)^x} = 1 \hfill \\
{3^x} = 1 \hfill \\
x = 0 \hfill \\
\end{gathered} \]

 

Пр.16

\[\begin{gathered}
{5^{2x}} - {7^x} - {5^{2x}} \cdot 35 + {7^x} \cdot 35 = 0 \hfill \\
{5^{2x}} - {5^{2x}} \cdot 35 = {7^x} - {7^x} \cdot 35 \hfill \\
{5^{2x}}\left( {1 - 35} \right) = {7^x}\left( {1 - 35} \right) \hfill \\
{5^{2x}} = {7^x}\left| { \div {7^x}} \right. \hfill \\
\frac{{{5^{2x}}}}{{{7^x}}} = 1 \hfill \\
\frac{{{{25}^x}}}{{{7^x}}} = 1 \hfill \\
{\left( {\frac{{25}}{7}} \right)^x} = 1 \hfill \\
x = 0 \hfill \\
\end{gathered} \]

 

Пр.17

\[\begin{gathered}
7 \cdot {3^{x + 1}} - {5^{x + 2}} = {3^{x + 4}} - {5^{x + 3}} \hfill \\
7 \cdot {3^x} \cdot 3 - {5^x} \cdot {5^2} = {3^x} \cdot {3^4} - {5^x} \cdot {5^3} \hfill \\
21 \cdot {3^x} - 25 \cdot {5^x} = 81 \cdot {3^x} - 125 \cdot {5^x} \hfill \\
21 \cdot {3^x} - 81 \cdot {3^x} = 25 \cdot {5^x} - 125 \cdot {5^x} \hfill \\
{3^x}\left( {21 - 81} \right) = {5^x}\left( {25 - 125} \right) \hfill \\
{3^x}\left( { - 60} \right) = {5^x}\left( { - 100} \right)\left| \div \right.{5^x}\left( { - 60} \right) \hfill \\
\frac{{{3^x}}}{{{5^x}}} = \frac{5}{3} \hfill \\
{\left( {\frac{3}{5}} \right)^x} = {\left( {\frac{3}{5}} \right)^{ - 1}} \hfill \\
x = - 1 \hfill \\
\end{gathered} \]

Call Now Button