Question

How do you solve question 5

Answer 1

log(x10)=14logx10=14Rewrite log(x10)=14logx10=14 in exponential form using the definition of a logarithm. If xx and bb are positive real numbers and bb≠≠11, then logb(x)=ylogbx=y is equivalent to by=xby=x.1014=x101014=x10Solve for xxTap for less steps...Raise 1010 to the power of 1414 to get 100000000000000100000000000000.100000000000000=x10100000000000000=x10Since xx is on the right side of the equation, switch the sides so it is on the left side of the equation.x10=1014x10=1014Multiply both sides of the equation by 1010.x=1014⋅(10)x=1014⋅10Simplify the right side.Tap for more steps...x=1000000000000000x=1000000000000000Verify each of the solutions by substituting them back into the original equation log(x)−log(10)=14logx-⁢log10=14 and solving. In this case, all solutions were found to be valid.x=1000000000000000

So here it is...COuld be a little sloppy

Answer 2

log properties

loga-logb=log(a/b)
and

$log_a(b)=c$ means $a^c=b$
and $log_a(a)=1$


if no base is written assume base 10
$log_{10}(x)-log_{10}(10)=14$
$log_{10}(x)-1=14$
add 1 to both sides
$log_{10}(x)=15$
translate
$10^{15}=x$
x=1,000,000,000,000,000