Question

Solve by rewriting as a logarithm and using a calculator. Round to the ne 4ˣ=3

Answer 1

To solve the equation 4ˣ=3 by rewriting as a logarithm and using a calculator, take the logarithm of both sides and divide the logarithm of 3 by the logarithm of 4.

Step-by-step explanation:

To solve the equation 4ˣ=3 by rewriting as a logarithm and using a calculator, we can take the logarithm of both sides of the equation. Since we want to round to the nearest decimal place, we will use the common logarithm (base 10). The equation becomes log(4ˣ) = log(3). Using a calculator, we can find the value of x by dividing the logarithm of 3 by the logarithm of 4.

x = log(3) / log(4)

Now, plug in the values in the calculator to find the result.

Answer 2

The equation
`4^x = 3` by rewriting it as a logarithm and using a calculator, you can use the change of base formula to convert log_4(3) into a form your calculator can handle. The value of x, when rounded to four decimal places, is approximately 0.7923.

The equation 4x = 3 by rewriting it as a logarithmic equation, you can use the logarithm base 4. The equation
`4^x = 3` can be expressed as: x = log4(3)

To find the numerical value of x, you can use a calculator. Most calculators have common logarithm (log base 10) and natural logarithm (ln or log base e) functions, but you can use the change of base formula to convert log4(3) into a form your calculator can handle. The change of base formula is: logb(a) = logc(a) / logc(b)

Let's use the change of base formula to rewrite log4(3) in terms of common logarithms: x = log(3) / log(4)

Now, you can input this expression into your calculator to find the approximate value of x. Rounding to four decimal places, the calculation would be:

x ≈ log(3) / log(4)

x ≈ 0.7923

Therefore, x ≈ 0.7923 when rounded to four decimal places.