Explicação passo a passo:
[tex]a)~~~log_{15}1=x\\ \\ 15^x=1\\ \\ 15^x=15^0\\ \\ cancela~~base~~15\\ \\ x=0\\ \\ \boxed{\log_{15}1=0}[/tex]
[tex]b)~~\log_{49}\sqrt{7} =x\\ \\ 49^x=\sqrt{7} \\ \\ 7^{2x}=7^{\frac{1}{2} }\\ \\ 2x=\dfrac{1}{2}\\ \\ 4x=1\\ \\ x=\dfrac{1}{4}\\ \\ \\\boxed{ \log_{49}\sqrt{7} =\dfrac{1}{4}}[/tex]
[tex]c)~~\log_4\dfrac{1}{64}=x\\ \\ \\ 4^x=\dfrac{1}{64}\\ \\ \\ 4^x=\dfrac{1}{4^3}\\ \\ \\ 4^x=4^{-3}\\ \\ x=-3\\ \\ \\\boxed{ \log_4\dfrac{1}{64}=-3}[/tex]
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Explicação passo a passo:
[tex]a)~~~log_{15}1=x\\ \\ 15^x=1\\ \\ 15^x=15^0\\ \\ cancela~~base~~15\\ \\ x=0\\ \\ \boxed{\log_{15}1=0}[/tex]
[tex]b)~~\log_{49}\sqrt{7} =x\\ \\ 49^x=\sqrt{7} \\ \\ 7^{2x}=7^{\frac{1}{2} }\\ \\ 2x=\dfrac{1}{2}\\ \\ 4x=1\\ \\ x=\dfrac{1}{4}\\ \\ \\\boxed{ \log_{49}\sqrt{7} =\dfrac{1}{4}}[/tex]
[tex]c)~~\log_4\dfrac{1}{64}=x\\ \\ \\ 4^x=\dfrac{1}{64}\\ \\ \\ 4^x=\dfrac{1}{4^3}\\ \\ \\ 4^x=4^{-3}\\ \\ x=-3\\ \\ \\\boxed{ \log_4\dfrac{1}{64}=-3}[/tex]