If anyone is good at logarithms pleas help me Solve for x, giving your answer to one decimal place, where necessary

x=  (2lg6+7)/(1-lg6)

x= (2*0.78+7)/(1-0.78)=8.56/0.22=38.9

Step-by-step explanation:

(x+2)lg 6=(x-7)lg10

but lg10=1

so x*lg6+2lg6=x-7

     -x*lg6         -x*lg6

2lg6=x-x*lg6-7

+7         +7

2lg6+7=x*(1-lg6)

so x=  (2lg6+7)/(1-lg6)

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.