Question

1)2^3х+3=42)5^х-4=6^х-4

Answer 1

2^3x=4
8x=4
x=4:8
x=0.5


5^x-4=6^x-4
5^x=6^x
5/6^x=1
5/6^x=5/6^0
x=0

Answer 2

To solve these equations, let's work through them step by step:

1. 2^(3x) + 3 = 42

Subtracting 3 from both sides, we have:

2^(3x) = 39

To isolate the exponent, we can take the logarithm (base 2) of both sides:

log2(2^(3x)) = log2(39)

Using the logarithmic property logb(a^c) = c * logb(a), we get:

3x * log2(2) = log2(39)

Simplifying:

3x = log2(39)

Finally, divide both sides by 3 to solve for x:

x = log2(39) / 3

2. 5^x - 4 = 6^x - 4

Subtracting -4 from both sides, we have:

5^x = 6^x

To eliminate the bases, we can take the logarithm (base 5) of both sides:

log5(5^x) = log5(6^x)

Using the logarithmic property logb(a^c) = c * logb(a), we get:

x * log5(5) = x * log5(6)

Since logb(b) = 1 for any base b, we have:

x = x * log5(6)

Dividing both sides by x (assuming x ≠ 0), we get:

1 = log5(6)

This equation implies that the logarithm of 6 to base 5 is equal to 1. In other words, x can be any real number since the equation is true for all values of x.