9^x-1=27^-x+2

9^x-1=27^-x+2

Question
Quadratics
asked 2021-02-08
\(\displaystyle{9}^{{x}}-{1}={27}^{{-{{x}}}}+{2}\)

Answers (1)

2021-02-09
We are given: \(\displaystyle{9}^{{x}}-{1}={27}^{{-{{x}}}}+{2}\)
Rewrite each base as a power of 3: \(\displaystyle{\left({3}^{{2}}\right)}^{{x}}-{1}={\left({3}^{{3}}\right)}^{{-{{x}}}}+{2}\)
Use the rule: \(\displaystyle{\left({a}^{{m}}\right)}^{{n}}={a}^{{m}}{n}\) \(\displaystyle{3}^{{{2}{\left({x}-{1}\right)}}}={3}^{{3}}^{\left(-{x}+{2}\right)}\)
Equate the exponents: 2(x-1)=3(-x+2)
Solve for x:
2x-2=-3x+8
2x=-3x+8
5x=8
\(\displaystyle{x}=\frac{{8}}{{5}}\) or 1.6
0

Relevant Questions

asked 2020-10-23
The equation \(\displaystyle{m}^{{\frac{{2}}{{3}}}}+{10}{m}^{{\frac{{1}}{{3}}}}+{9}={0}\) is said to be in __________form, because making the substitution u = __________results in a new equation that is quadratic.
asked 2021-01-31
Solve the quadratic by using the quadratic formula x^2 = 7x + 9
asked 2021-01-30
A function is a ratio of quadratic functions and has a vertical asymptote x =4 and just one -intercept, x =1. It is known f that has a removable discontinuity at x =- 1 and \(\displaystyle\lim_{{{x}\to{1}}}{f{{\left({x}\right)}}}={2}\). Evaluate
a) f(0)
b) \(\displaystyle\lim{x}_{{{x}\to\infty}}{f{{\left({x}\right)}}}\)
asked 2021-03-08
Find the roots of the function
\(\displaystyle{f{{\left({x}\right)}}}={\left({2}{x}−{1}\right)}\cdot{\left({x}^{{2}}+{2}{x}−{3}\right)}\), with \(\displaystyle{x}\in{R}\)
asked 2021-02-14
Multiply and simplify
\(\displaystyle\frac{{{x}^{{2}}+{2}{x}-\frac{{3}}{{x}^{{2}}}+{1}{x}-{20}}}{{{x}-\frac{{1}}{{x}}+{5}}}\)
asked 2020-12-25
A quadratic function has its vertex at the point (1,6). The function passes through the point (-2, -3). Find the quadratic and linear coefficients and the constant team of the function.
- The quadratic coefficients is
- The linear coefficients is
- The constant term is
asked 2020-12-22
A quadratic function has its vertex at the point (1,6). The function passes through the point (-2, -3). Find the quadratic and linear coefficients and the constant team of the function.
-The quadratic coefficients is
-The linear coefficients is
-The constant term is
asked 2021-03-02
Express \(\displaystyle{x}^{{{2}}}+{8}{x}\) \ in the form \ \(\displaystyle{\left({x}+{a}\right)}{2}+{b}\)
asked 2020-10-25
Solve the following quadratic equation \(\displaystyle{6}{x}^{{2}}-{x}-{15}={0}\)
asked 2020-12-03
Solve quadratic equation using the quadratic formula. \(\displaystyle{x}^{{2}}+{5}{x}+{2}={0}\)
...