Solve for x in the equation 3^x - 2^x = 65

Answer

The given equation is

We can try integer values for

to find a solution.

.
If

Thus,

is a solution.

Let

.
The derivative of

.
Since

and

are always positive, and

, the derivative

is positive when

is large enough.
When

.
When

Since

for

is an increasing function for

.
Therefore,

is the only solution.

Final Answer: The final answer is

Related math solutions

Joint Variation Word Problem: Calculating Kinetic Energy

Learn how to model joint variation, find the constant of proportionality, and calculate kinetic energy given mass and velocity. Follow step-by-step algebra work to solve for joules.

Solve (x^2 + x)/x = 8 and Find 2√x | Rational Equation Solution

Simplify the rational expression (x^2 + x)/x by factoring out x to get x + 1, then solve x + 1 = 8 to find x = 7, so 2√x = 2√7 ≈ 5.29.

Solving a Cubic Equation by Factoring

This problem involves solving the cubic equation 2x^3 + 2x^2 - 24x = 0 by factoring out the greatest common factor and then factoring the resulting quadratic expression.

Algebraic Proof: Show That an Expression is Even

Prove algebraically that the expression n^2 - 2 - (n - 2)^2 is always an even number by expanding the brackets and factoring out a 2.

Rewrite y + 7 = 1/5(x + 10) in Slope-Intercept Form

Learn how to convert the linear equation y + 7 = 1/5(x + 10) into slope-intercept form by distributing and isolating y to get y = 1/5x - 5.

Solve for x in the equation 3^x - 2^x = 65

Question

Answer

Related math solutions

Débloquez la version web à vie

Related math solutions