Answer to Question #192674 in Algebra for will

Question

Solving Exponential Equations Practice:

1. 8^x-3 =8⁵
2. 10^3x+2 = 10¹¹
3. 4^6x = 16⁹

Answer 1

1.

$8^{x-3}=8^5$

Exponential equation function is monotone

$x-3=5$

$x=8$

2.

$10^{3x+2}=10^{11}$

Exponential equation function is monotone

$3x+2=11$

$3x=9$

$x=3$

3.

$4^{6x}=16^9$

$4^{6x}=(4^2)^9$

$4^{6x}=4^{2\cdot9}$

$4^{6x}=4^{18}$

Exponential equation function is monotone

$6x=18$

$x=3$