kadejoset

Answered

2022-07-28

1. How many real numbers x satisfy the equation $\frac{1}{5}{\mathrm{log}}_{2}x=\mathrm{sin}(5\pi x)$?

2. Find the value of x that satisfies ${\mathrm{log}}_{x}25-{\mathrm{log}}_{x}4={\mathrm{log}}_{x}\sqrt{x}$

3. Find the numerical value of ${\mathrm{log}}_{\frac{1}{125}}{25}^{3}\sqrt{25}$.

2. Find the value of x that satisfies ${\mathrm{log}}_{x}25-{\mathrm{log}}_{x}4={\mathrm{log}}_{x}\sqrt{x}$

3. Find the numerical value of ${\mathrm{log}}_{\frac{1}{125}}{25}^{3}\sqrt{25}$.

Answer & Explanation

Hassan Watkins

Expert

2022-07-29Added 18 answers

How many real numbers x satisfy the equation

${\mathrm{log}}_{2}({x}^{1/5})=\mathrm{sin}(5\pi x)\mathrm{sin}(5\pi x)$ is always 0.

${2}^{\mathrm{sin}(5\pi x)}={x}^{1/5}\Rightarrow {2}^{0}={x}^{1/5}\Rightarrow x=1$

2. Find the value of x that satisfies .

${\mathrm{log}}_{x}(25/4)={\mathrm{log}}_{x}({x}^{1/2})\Rightarrow 25/4=\sqrt{x}\Rightarrow x=625/16$

3. Find the numerical value of.

$={\mathrm{log}}_{{5}^{-3}}{5}^{2}{5}^{2/3}={\mathrm{log}}_{{5}^{-3}}{5}^{8/3}=-8/9$

${\mathrm{log}}_{2}({x}^{1/5})=\mathrm{sin}(5\pi x)\mathrm{sin}(5\pi x)$ is always 0.

${2}^{\mathrm{sin}(5\pi x)}={x}^{1/5}\Rightarrow {2}^{0}={x}^{1/5}\Rightarrow x=1$

2. Find the value of x that satisfies .

${\mathrm{log}}_{x}(25/4)={\mathrm{log}}_{x}({x}^{1/2})\Rightarrow 25/4=\sqrt{x}\Rightarrow x=625/16$

3. Find the numerical value of.

$={\mathrm{log}}_{{5}^{-3}}{5}^{2}{5}^{2/3}={\mathrm{log}}_{{5}^{-3}}{5}^{8/3}=-8/9$

Most Popular Questions