To find the x-intercept(s), substitute in <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Solve the equation.

Rewrite the equation as <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> in exponential form using the definition of a logarithm. If <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> are positive real numbers and <math><mstyle displaystyle="true"><mi>b</mi><mo>≠</mo><mn>1</mn></mstyle></math> , then <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>y</mi></mstyle></math> is equivalent to <math><mstyle displaystyle="true"><msup><mrow><mi>b</mi></mrow><mrow><mi>y</mi></mrow></msup><mo>=</mo><mi>x</mi></mstyle></math> .

Solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Rewrite the equation as <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msup></mstyle></math> .

Anything raised to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the equation.

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></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> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

x-intercept(s) in point form.

x-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math>

x-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math>

To find the y-intercept(s), substitute in <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Solve the equation.

Remove parentheses.

Simplify <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mn>2</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

y-intercept(s) in point form.

y-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><msub><mi>log</mi><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math>

y-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><msub><mi>log</mi><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math>

List the intersections.

x-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math>

y-intercept(s): <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><msub><mi>log</mi><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math>

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