0\; ,\\\\2^{log_3x}\cdot 2^3-5\cdot x^{log_32}-24=0\\\\\\\star a^{log_{b}c}=\Big [\; a=c^{log_{c}a}\; \Big ]=\Big (c^{log_{c}a}\Big )^{log_{b}c}=c^{log_{c}a\, \cdot \, log_{b}c}=\Big [\; log_{b}c=\frac{1}{log_{c}b}\; \Big ]=\\\\=c^{\frac{log_{c}a}{log_{c}b}}=\Big [\; log_{b}a=\frac{log_{c}a}{log_{c}b}\; \Big ]=c^{log_{b}a}\; \; \Rightarrow \; \; \boxed {a^{log_{b}c}=c^{log_{b}a}}\; \; \star \\\\\\8\cdot 2^{log_3x}-5\cdot 2^{log_3x}-24=0" alt="2^{log_3x+3}-5\cdot x^{log_32}-24=0\; ,\; \; ODZ:\; x>0\; ,\\\\2^{log_3x}\cdot 2^3-5\cdot x^{log_32}-24=0\\\\\\\star a^{log_{b}c}=\Big [\; a=c^{log_{c}a}\; \Big ]=\Big (c^{log_{c}a}\Big )^{log_{b}c}=c^{log_{c}a\, \cdot \, log_{b}c}=\Big [\; log_{b}c=\frac{1}{log_{c}b}\; \Big ]=\\\\=c^{\frac{log_{c}a}{log_{c}b}}=\Big [\; log_{b}a=\frac{log_{c}a}{log_{c}b}\; \Big ]=c^{log_{b}a}\; \; \Rightarrow \; \; \boxed {a^{log_{b}c}=c^{log_{b}a}}\; \; \star \\\\\\8\cdot 2^{log_3x}-5\cdot 2^{log_3x}-24=0" align="absmiddle" class="latex-formula">
