Answer:
6^x +2 = 10^x +7
First take logarithm to base 6 to both sides
That's
log 6 6^x+2 = log 6 10^x+7
We get
x + 2 = log 6 (10) x - 7log 6 10
Move the constants to the right side of the equation
We get
x - log 6 (10)x = - 7log 6 (10) - 2
Factor out x from the expression
We get
( 1 - log 6 (10)x = - 7 log 6 (10) - 2
Divide both sides by 1 - log 6 (10)
We get
x = - 7 log 6 (10) - 2 / 1 - log 6 (10)
Rewrite the expression
x = log 6 (10^-7) - log 6 ( 6^-2) / log 6 (6) - log 6 (10)
Simply the expression
x = log 6 ( 10^-7 × 6^-2)/ log 6 (6/10)
x = log 6 ( 1 / 36 × 10^7) / log 6 (3/5)
Using log b (x) / log b (a) = log a (x)
Write the expression as
x = log 3/5 ( 36 × 10^-7)
x = - log 3/5 ( 36 × 10^7)
x = 38.568
Hope this helps.
Please give Branliest.
