Question

Solve for x. Round to the nearest ten thousandths 4^x=10

Answer 1

Answer:

1.6610

Step-by-step explanation:

1) To solve for x, isolate it in the equation. Notice that x is an exponent in this equation. To change that, take the logarithm of both sides:

$4^x = 10 \\log4^x = log10$

2) Now, using the power property of logarithms, bring the x out in front like so:

$log4^x = log10\\xlog4 = log 10$  

3) Now, to finally isolate x, divide both sides by $log4$:

$xlog4 = log10\\\frac{xlog4}{log4} =\frac{log10}{log4}$

$x = \frac{log10}{log4}$

4) Now, put that found value for x into the calculator. Round the answer to the ten thousandths place, or the fourth digit from the right of the decimal point. This gives the answer 1.6610.