How do you solve #7^(2x-3) - 4 = 14# and find any extraneous solutions?

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Answer 1 · 2018-05-31T12:22:52

Solution: # x~~ 2.243 #

# 7^(2 x-3) - 4 =14# or

# 7^(2 x-3) =18# Taking log on both sides we get,

# (2 x-3) log 7 = log 18# or

# (2 x-3) = log 18/log 7 # or

# (2 x-3) = log 18/log 7 ~~ 1.485# or

# 2 x ~~ 3+ 1.485 ~~ 4.485# or

# x ~~ 4.485/2 ~~ 2.243(2 dp)#

Check: # 7^(2 *2.243-3) - 4 ~~ 14#(verified)

No extraneous solution.

Solution: # x~~ 2.243 (3 dp) # [Ans]