Solve asqrt[x]{sqrt[6]{10}}=sqrt[24]{10}

$$a \sqrt[ x ] { \sqrt[ 6 ] { 10 } } = \sqrt[ 24 ] { 10 }$$

Solve for a

$$a=10^{\frac{1}{24}-\frac{1}{6x}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sqrt[x]{\sqrt[6]{10}}a=\sqrt[24]{10}$$

Divide both sides by \sqrt[x]{\sqrt[6]{10}}.

$$\frac{\sqrt[x]{\sqrt[6]{10}}a}{\sqrt[x]{\sqrt[6]{10}}}=\frac{\sqrt[24]{10}}{\sqrt[x]{\sqrt[6]{10}}}$$

Dividing by \sqrt[x]{\sqrt[6]{10}} undoes the multiplication by \sqrt[x]{\sqrt[6]{10}}.

$$a=\frac{\sqrt[24]{10}}{\sqrt[x]{\sqrt[6]{10}}}$$

Divide \sqrt[24]{10} by \sqrt[x]{\sqrt[6]{10}}.

$$a=10^{\frac{1}{24}-\frac{1}{6x}}$$

Solve for x

$$x=-\frac{4\ln(10)}{24\ln(a)-\ln(10)}$$

$$a\neq \sqrt[24]{10}\text{ and }a>0$$