Solving Exponential Equations

solving equations with same base

100

solve for x 

2^{x + 6} = 32 

x=-1

200

 9^{2x – 5}= 27

x = 13/4

300

2^7x X 8 = 256^x

x=3 

400

9^-3x+2 x 3^-3 = 27^-2x-1

x=7

500

4^5−9x=1/8x−2

x=4/15 

vocab

100

what is b called in this situation

b^x=b^y

base 

200

what is x called

b^x

exponent 

300

what is the name of the a solution that is written as a complex fraction that contains a log 

exact solution 

400

what is the name of the solution that is gotten from calculating the exact solution  

approximate solution 

500

what are the two methods called for solving exponential equations 

same base method and solving with logs method

formulas

100

what formula represents the solving with the same base method 

b^x=b^y

200

if b^x=b^y  what is true about x and y 

x=y 

300

what is the exponential format  

b^x=a 

400

what is the logarithmic format 

log_ba=x

facts about the process

100

if one side has a base of 5 and the other side has base of 25 what method should be used 

same base method 

200

if there is a 8^x+2 on one side and 512 on the other side of the equation what should 512 be rewritten as 

8³ 

300

what is 7⁵=16807 in logarithmic form 

log₇16807=5

400

what method be used to solve 5^3x+7=311 

solving with logs 

500

what is 7^5x+3 = 312 in log form 

log(7^5x+3 )= log(312)

solving equations with logs

100

5^2x=21

x=log₅(21) / 2 = 0.9458 

200

(e^4x−3/e^x-2)−7=13

x= ln(10)+1/ 3 or 1.1009 

300

10^x+5-8=60 

x=log(68)-5 or -3.167

400

5 X 2^x=240 

x= og(48)/log(2) or 5.585 

500

2 X 6^x = 236 

x= log₆(118) or 2.6626