Question

use the like-bases property and exponents to solve the equation
\\6(10)^x - 15 = 59985\\

\\x =\\

Explanation:

Step1: Isolate the exponential term

Add \(15\) to both sides of the equation.

$$6(10)^{x} = 59985 + 15$$

$$6(10)^{x} = 60000$$

Step2: Divide by the coefficient

Divide both sides by \(6\).

$$(10)^{x} = \frac{60000}{6}$$

$$10^{x} = 10000$$

Step3: Express with like bases

Write \(10000\) as a power of \(10\).

$$10^{x} = 10^{4}$$

Step4: Solve for the variable

Equate the exponents since the bases are equal.

$$x = 4$$

Answer:

\(x = 4\)