Explicação passo-a-passo:
[tex] log_{10}(0.0001) = x[/tex]
[tex] {10}^{x} = 0.0001[/tex]
[tex] {10}^{x} = {10}^{ - 4} [/tex]
[tex] \: \: \: x = - 4[/tex]
============================
[tex] log_{5}( \sqrt{5} ) = x[/tex]
[tex] {5}^{x} = \sqrt{5} [/tex]
[tex] {5}^{x} = {5}^{ \frac{1}{2} } [/tex]
[tex] \: \: \: x = \frac{1}{2} [/tex]
[tex] log_{2}( \sqrt[3]{4} ) = x[/tex]
[tex] {2}^{x} = \sqrt[3]{4} [/tex]
[tex] {2}^{x} = {4}^{ \frac{1}{3} } [/tex]
[tex] {2}^{x} = ( { {2}^{2}) }^{ \frac{1}{3} } [/tex]
[tex] {2}^{x} = {2}^{ \frac{2}{3} } [/tex]
[tex] \: \: \: x = \frac{2}{3} [/tex]
================================
.
[tex]portanto...[/tex]
===============================
[tex] - 4 + \frac{1}{2} - \frac{2}{3} = [/tex]
[tex] - \frac{24}{6} + \frac{3}{6} - \frac{4}{6} = [/tex]
[tex] \: \: \: \: \: \frac{ - 24 \: + \: 3 \: - \: 4}{6} = [/tex]
[tex] \: \: \: \: \: \: \: \frac{ - 21 \: - \: 4}{6} = [/tex]
[tex] \: \: \: \: \: \: \: \: \: - \frac{25}{6} [/tex]
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Explicação passo-a-passo:
[tex] log_{10}(0.0001) = x[/tex]
[tex] {10}^{x} = 0.0001[/tex]
[tex] {10}^{x} = {10}^{ - 4} [/tex]
[tex] \: \: \: x = - 4[/tex]
============================
[tex] log_{5}( \sqrt{5} ) = x[/tex]
[tex] {5}^{x} = \sqrt{5} [/tex]
[tex] {5}^{x} = {5}^{ \frac{1}{2} } [/tex]
[tex] \: \: \: x = \frac{1}{2} [/tex]
============================
[tex] log_{2}( \sqrt[3]{4} ) = x[/tex]
[tex] {2}^{x} = \sqrt[3]{4} [/tex]
[tex] {2}^{x} = {4}^{ \frac{1}{3} } [/tex]
[tex] {2}^{x} = ( { {2}^{2}) }^{ \frac{1}{3} } [/tex]
[tex] {2}^{x} = {2}^{ \frac{2}{3} } [/tex]
[tex] \: \: \: x = \frac{2}{3} [/tex]
================================
.
[tex]portanto...[/tex]
===============================
[tex] - 4 + \frac{1}{2} - \frac{2}{3} = [/tex]
[tex] - \frac{24}{6} + \frac{3}{6} - \frac{4}{6} = [/tex]
[tex] \: \: \: \: \: \frac{ - 24 \: + \: 3 \: - \: 4}{6} = [/tex]
[tex] \: \: \: \: \: \: \: \frac{ - 21 \: - \: 4}{6} = [/tex]
[tex] \: \: \: \: \: \: \: \: \: - \frac{25}{6} [/tex]