Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

Expand <math><mstyle displaystyle="true"><mi>ln</mi><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>x</mi></mrow></msup><mo>)</mo></mrow></mstyle></math> by moving <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> outside the logarithm.

Divide each term in <math><mstyle displaystyle="true"><mi>x</mi><mi>ln</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo>=</mo><mi>ln</mi><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mi>ln</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mi>ln</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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