Home > Algebra > Variable Expressions

How do you solve for x?: #log_6 (36) = 5x + 3#

Answer 1

Avery Alexander

#x=-1/5#

By applying the laws of exponents and the definition of logs, we can express this equation exponentially as

#6^(5x+3)=36#

#therefore6^(5x)*6^3=6^2#

#therefore5x+3=2=>-1/5#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Savannah Anderson

To solve for ( x ), use the property of logarithms: ( \log_a (b) = c ) is equivalent to ( a^c = b ). Apply this property to ( \log_6 (36) = 5x + 3 ). So, ( 6^{5x + 3} = 36 ). Simplify and solve for ( x ). ( 6^{5x + 3} = 6^2 ) → ( 5x + 3 = 2 ) → ( 5x = -1 ) → ( x = -\frac{1}{5} ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.