Đáp án:
e) x=5
f) x=4
g)x=-2
f)\(
\left[ {\begin{array}{*{20}c}
{x = \frac{1}{2}} \\
{x = \frac{1}{4}} \\
\end{array}} \right.
\)
Giải thích các bước giải:
\(
\begin{array}{l}
e)2.3^x - 405 = 3^{x - 1} \\
\Leftrightarrow 2.3^x - 405 = \frac{{3^x }}{3} \\
\Leftrightarrow 6.3^x - 1215 = 3^x \\
\Leftrightarrow 5.3^x = 1215 \\
\Leftrightarrow 3^x = 243 \\
\Leftrightarrow x = 5 \\
f)(\frac{1}{{81}})^x .27^{2x} = ( - 9)^4 \\
\Leftrightarrow (\frac{1}{{3^4 }})^x .(3^3 )^{2x} = 9^4 \\
\Leftrightarrow \frac{1}{{3^{4x} }}.3^{6x} = (3^2 )^4 \\
\Leftrightarrow 3^{2x} = 3^8 \\
\Leftrightarrow 2x = 8 \\
\Leftrightarrow x = 4 \\
g)5^x (5^3 )^2 = 625 \\
\Leftrightarrow 5^x .5^6 = 5^4 \\
\Leftrightarrow 5^{x + 6} = 5^4 \\
\Leftrightarrow x + 6 = 4 \\
\Leftrightarrow x = - 2 \\
h)(4x - 1)^{30} = (4x - 1)^{20} \\
\Leftrightarrow \left[ {\begin{array}{*{20}c}
{4x - 1 = 1} \\
{4x - 1 = 0} \\
\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}c}
{x = \frac{1}{2}} \\
{x = \frac{1}{4}} \\
\end{array}} \right. \\
\end{array}
\)
